Question

Presented below are three unrelated situations.

(a) Dwayne Wade Company recently signed a lease for a new office building, for a lease period of 10 years. Under the lease agreement, a security deposit of \(12,000 is made, with the deposit to be returned at the expiration of the lease, with interest compounded at 5% per year. What amount will the company receive at the time the lease expires?

(b) Serena Williams Corporation, having recently issued a \)20 million, 15-year bond issue, is committed to make annual sinking fund deposits of \(600,000. The deposits are made on the last day of each year and yield a return of 10%. Will the fund at the end of 15 years be sufficient to retire the bonds? If not, what will the deficiency be?

(c) Under the terms of his salary agreement, president Rex Walters has an option of receiving either an immediate bonus of \)55,000, or a deferred bonus of $70,000 payable in 10 years. Ignoring tax considerations and assuming a relevant interest rate of 4%, which form of settlement should Walters accept?

Short answer

The company will receive the $19,547 at expiration, the deficiency will be $936,512, and Rex should opt for the immediate bonus of amount $55,000.

Step-by-step solution

Computation amount received

$\begin{array}{rcl}\mathrm{Amount}\mathrm{Received}& =& \mathrm{Amount}\times \mathrm{FV}\\ & =& 12,000\times 1.62889\\ & =& \$19,547\end{array}$

Calculation of the deficiency

$\begin{array}{rcl}\mathrm{FV}\mathrm{of}\mathrm{ordinary}\mathrm{annuity}& =& \mathrm{Amount}\times \mathrm{FV}\mathrm{factor}\\ & =& 600,000\times 31.77248\\ & =& 19,063,488\end{array}$

$\begin{array}{rcl}\mathrm{Deficiency}& =& \mathrm{Issue}\mathrm{price}\mathrm{of}\mathrm{bond}-\mathrm{amount}\mathrm{calculated}\\ & =& 20,000,000-19,063,488\\ & =& \$936,512\end{array}$

Calculation of present value of the deferred bonus

$\begin{array}{rcl}\mathrm{PV}\mathrm{of}\mathrm{deferred}\mathrm{bonus}& =& \mathrm{Bonus}\mathrm{amount}\times \mathrm{PV}\mathrm{factor}\\ & =& 70,000\times 0.67556\\ & =& \$47,289\end{array}$

He should opt for the immediate bonus of $55,000.