Question

Hill Company operates a chain of sandwich shops. The company is considering two possible expansion plans. Plan A would open eight smaller shops at a cost of$8,700,000.Expectedannualnetcashinflowsare$1,550,000 for 10 years, with zeroresidual value at the end of 10 years. Under Plan B, Hill Company would open threelarger shops at a cost of $8,340,000.Thisplanisexpectedtogeneratenetcashinflowsof$990,000 per year for 10 years, the estimated useful life of the properties. Estimatedresidual value for Plan B is $1,200,000. Hill Company uses straight-line depreciationand requires an annual return of 10%.

Requirements

1. Compute the payback, the ARR, the NPV, and the profitability index of thesetwo plans.

2. What are the strengths and weaknesses of these capital budgeting methods?

3. Which expansion plan should Hill Company choose? Why?

4. Estimate Plan A’s IRR. How does the IRR compare with the company’s requiredrate of return?

Short answer

NPV for project A:$824,130

NPV for Project B:-$1,793,646

Step-by-step solution

Computation of CB ratios

Computation for Project A

Payback period

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{=}\frac{\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}{\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{5}\mathbf{.}\mathbf{613}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

ARR

$\begin{array}{c}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{=}\frac{\mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{-}\mathbf{R}\mathbf{e}\mathbf{s}\mathbf{i}\mathbf{d}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{U}\mathbf{s}\mathbf{e}\mathbf{f}\mathbf{u}\mathbf{l}\mathbf{L}\mathbf{i}\mathbf{f}\mathbf{e}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{0}}{\mathbf{10}}\\ \mathbf{=}\mathbf{\$}\mathbf{870}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{870}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{680}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}{\mathbf{2}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}}{\mathbf{2}}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{350}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{680}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{350}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{156}\mathbf{o}\mathbf{r}\mathbf{15}\mathbf{.}\mathbf{6}\mathbf{\%}\end{array}$

NPV

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{I}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+r\right)}^n}}{r}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+0.1\right)}^{10}}}{0.1}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{1446}\\ \mathbf{=}\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{524}\mathbf{,}\mathbf{130}\end{array}$

$\begin{array}{c}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\mathbf{-}\mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{524}\mathbf{,}\mathbf{130}\mathbf{-}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{824}\mathbf{,}\mathbf{130}\end{array}$

Profitability index

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{524}\mathbf{,}\mathbf{130}}{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{095}\end{array}$

Computation for Project B

Payback period

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{=}\frac{\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}{\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{340}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{990}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{8}\mathbf{.}\mathbf{4242}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

ARR

$\begin{array}{c}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{=}\frac{\mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{-}\mathbf{R}\mathbf{e}\mathbf{s}\mathbf{i}\mathbf{d}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{U}\mathbf{s}\mathbf{e}\mathbf{f}\mathbf{u}\mathbf{l}\mathbf{L}\mathbf{i}\mathbf{f}\mathbf{e}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{340}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{10}}\\ \mathbf{=}\mathbf{\$}\mathbf{714}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\\ \mathbf{=}\mathbf{\$}\mathbf{990}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{714}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{276}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}{\mathbf{2}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{340}\mathbf{,}\mathbf{000}}{\mathbf{2}}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{170}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{276}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{170}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0662}\mathbf{o}\mathbf{r}\mathbf{6}\mathbf{.}\mathbf{62}\mathbf{\%}\end{array}$

NPV

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{I}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+r\right)}^n}}{r}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{990}\mathbf{,}\mathbf{000}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+0.1\right)}^{10}}}{0.1}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{990}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{145}\\ \mathbf{=}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{083}\mathbf{,}\mathbf{550}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{i}\mathbf{d}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{R}\mathbf{e}\mathbf{s}\mathbf{i}\mathbf{d}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{\times }{\left[\frac{1}{1+r}\right]}^{\mathbf{n}}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{\times }{\left[\frac{1}{1+0.1}\right]}^{\mathbf{10}}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{386}\\ \mathbf{=}\mathbf{\$}\mathbf{463}\mathbf{,}\mathbf{200}\end{array}$

$\begin{array}{c}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\mathbf{-}\mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{083}\mathbf{,}\mathbf{154}\mathbf{+}\mathbf{\$}\mathbf{463}\mathbf{,}\mathbf{200}\mathbf{-}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{340}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{793}\mathbf{,}\mathbf{646}\end{array}$

Profitability index

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{083}\mathbf{,}\mathbf{154}\mathbf{+}\mathbf{\$}\mathbf{463}\mathbf{,}\mathbf{200}}{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{340}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{785}\end{array}$

 Step 2: Strength and weaknesses of Capital Budgeting

Strength of capital budgeting methods

1. Payback –i) Simplest method

ii) Helpful in determine g the risk in terms of cost recovery period

2. ARR –i) Uses the accounting profit

ii) Measures the profitability over asset’s life

3. NPV–i) Provides the time value of money

ii) Measures the earning capability against the minimum required rate of return

4. IRR–i) Computes the actual rate of return

ii) Considers net cash flow over assets entire life

Weaknesses of capital budgeting methods

1. Payback –i) Ignores time value of money

ii) Do not take consideration of cash flow after payback period

2. ARR –i) Do not use time value of money

ii) Only takes accounting profit concept

3. NPV–i) Complex method

ii) Requires specialized skill for the use of the method

4. IRR–i) Complex and difficult method

ii) Not relevant in all conditions

Recommendation

Based on the above analysis, project A provides a good positive NPV of $824,130. Whereas, project B provides a negative NPV. The payback period for project B is also high in comparison to project A. Furthermore, there is also a risk of the collection period.

So, based on these facts and figures project A is recommended

Computation of IRR

IRR

IRR is the rate at which the present value of cash inflow equals initial investment.

Let’s say IRR = R%

Then,

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\\ \mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{I}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+r\right)}^n}}{r}\right]\\ \mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{700}\mathbf{,}\mathbf{000}\mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{\times }\left[\frac{1-\frac{1}{{\left(1+R\right)}^{10}}}{R}\right]\\ \mathbf{5}\mathbf{.}\mathbf{6129}\mathbf{=}\left[\frac{1-\frac{1}{{\left(1+R\right)}^{10}}}{R}\right]\end{array}$

By hit and trial method if R is taken 12.25% for 10 years then,

$\begin{array}{c}\mathbf{5}\mathbf{.}\mathbf{6}\mathbf{=}\left[\frac{1-\frac{1}{{\left(1+0.1225\right)}^{10}}}{0.1225}\right]\\ \mathbf{5}\mathbf{.}\mathbf{6}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{59}\end{array}$

So the IRR = 12.25%

As compared to required rate of return, IRR is only 2% above the RRR. It means that the project’s NPV would be positive but with lesser degree.