Question

Answer each of these unrelated questions.

(a) On January 1, 2017, Fishbone Corporation sold a building that cost \(250,000 and that had accumulated depreciation of \)100,000 on the date of sale. Fishbone received as consideration a \(240,000 non-interest-bearing note due on January 1, 2020. There was no established exchange price for the building, and the note had no ready market. The prevailing rate of interest for a note of this type on January 1, 2017, was 9%. At what amount should the gain from the sale of the building be reported?

(b) On January 1, 2017, Fishbone Corporation purchased 300 of the \)1,000 face value, 9%, 10-year bonds of Walters Inc. The bonds mature on January 1, 2027, and pay interest annually beginning January 1, 2018. Fishbone purchased the bonds to yield 11%. How much did Fishbone pay for the bonds?

(c) Fishbone Corporation bought a new machine and agreed to pay for it in equal annual installments of \(4,000 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 8% applies to this contract, how much should Fishbone record as the cost of the machine?

(d) Fishbone Corporation purchased a special tractor on December 31, 2017. The purchase agreement stipulated that Fishbone should pay \)20,000 at the time of purchase and \(5,000 at the end of each of the next 8 years. The tractor should be recorded on December 31, 2017, at what amount, assuming an appropriate interest rate of 12%?

(e) Fishbone Corporation wants to withdraw \)120,000 (including principal) from an investment fund at the end of each year for 9 years. What should be the required initial investment at the beginning of the first year if the fund earns 11%?

Short answer

The gain on the sale of the building is $35,323.

The amount paid for bonds is $264,663.

PV of ordinary annuity for part C is$26,840.

The cost of the tractor to be recorded is $44,838.

The PV of ordinary annuity for part E is $664,446

Step-by-step solution

Calculation of gain on sale of the building

.$\begin{array}{rcl}\mathbf{Present}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Future}\mathbf{}\mathbf{Value}\mathbf{\times }\mathbf{PVF}\\ & \mathbf{=}& \mathbf{240}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{77218}\\ & \mathbf{=}& \mathbf{\$}\mathbf{185}\mathbf{,}\mathbf{323}\\ & & \end{array}$

$$\begin{gathered} \mathbf{Gain}\mathbf{}\mathbf{}\mathbf{on}\mathbf{}\mathbf{}\mathbf{sale}\mathbf{}\mathbf{of}\mathbf{}\mathbf{building}\mathbf{=}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Note}\mathbf{-}\mathbf{Book}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{building} \\ \mathbf{=}\mathbf{185}\mathbf{,}\mathbf{323}\mathbf{-}\mathbf{(}\mathbf{250000}\mathbf{-}\mathbf{100}\mathbf{,}\mathbf{000}\mathbf{)} \\ \mathbf{=}\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{323} \end{gathered}$$

Calculation of amount paid for bonds

$\begin{array}{rcl}\mathbf{Amount}\mathbf{}\mathbf{paid}\mathbf{}\mathbf{for}\mathbf{}\mathbf{bonds}& \mathbf{=}& \mathbf{Present}\mathbf{}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{received}\mathbf{}\mathbf{and}\mathbf{}\mathbf{principal}\mathbf{}\mathbf{amount}\\ & \mathbf{=}& \mathbf{300}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{35218}\mathbf{+}\mathbf{27}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{5}\mathbf{.}\mathbf{88923}\\ & \mathbf{=}& \mathbf{\$}\mathbf{264}\mathbf{,}\mathbf{663}\\ & & \end{array}$

Computation of PV of an ordinary annuity

$\begin{array}{rcl}\mathbf{PV}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{}\mathbf{annuity}& \mathbf{=}& \mathbf{Rents}\mathbf{\times }\mathbf{PVF}\mathbf{-}\mathbf{OA}\\ & \mathbf{=}& \mathbf{4}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{71008}\\ & \mathbf{=}& \mathbf{\$}\mathbf{26}\mathbf{,}\mathbf{840}\\ & & \end{array}$

Computation of total cost of tractor

$\begin{array}{rcl}\mathbf{Amount}\mathbf{}\mathbf{of}\mathbf{}\mathbf{tractor}\mathbf{}\mathbf{to}\mathbf{}\mathbf{be}\mathbf{}\mathbf{recorded}& \mathbf{=}& \mathbf{Amount}\mathbf{}\mathbf{paid}\mathbf{}\mathbf{at}\mathbf{}\mathbf{pruchase}\mathbf{+}\mathbf{PV}\mathbf{}\mathbf{or}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{annuity}\\ & \mathbf{=}& \mathbf{20}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{4}\mathbf{.}\mathbf{96764}\\ & \mathbf{=}& \mathbf{\$}\mathbf{44}\mathbf{,}\mathbf{838}\\ & & \end{array}$

Computation of PV of an ordinary annuity

$\begin{array}{rcl}\mathbf{PV}\mathbf{}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{annuity}& \mathbf{=}& \mathbf{Rents}\mathbf{\times }\mathbf{PVF}\mathbf{-}\mathbf{OA}\\ & \mathbf{=}& \mathbf{120}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{5}\mathbf{.}\mathbf{53705}\\ & \mathbf{=}& \mathbf{\$}\mathbf{664}\mathbf{,}\mathbf{446}\\ & & \end{array}$