Question

1. Steve Fowler borrowed $94,900 on March 1, 2018. This amount plus accrued interest at 6% compounded semiannually is to be repaid March 1, 2028. To retire this debt, Steve plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2023, and for the next 4 years. The fund is expected to earn 5% per annum.

How much must be contributed each year by Steve Fowler to provide a fund sufficient to retire the debt on March 1, 2028? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,583.)

Annual contribution to debt retirement fund

$

2. Assume that Sonic Foundry Corporation has a contractual debt outstanding. Sonic has available two means of settlement. It can either make immediate payment of $2,072,000, or it can make annual payments of $283,200 for 15 years.

Payments must begin now and be made on the first day of each of the 15 years, what payment method would you recommend assuming an expected effective-interest rate of 11% during the future period? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Present value of annual payment		$
Recommended payment method		Annual PaymentsImmediate Payment

3.

Alan Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 3 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 3 years, by conducting some research online, Alan has developed the following estimates.

Engine Overhaul Estimated Cash Outflow			Probability Assessment
$270			10%
570			30%
720			50%
920			10%

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How much should Alan Bowie deposit today in an account earning 9%, compounded annually, so that he will have enough money on hand in 3 years to pay for the overhaul? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Deposit amount

$enter the deposit amount in dollars rounded to 0 decimal places

4.Teal Inc. manufactures cycling equipment. Recently, the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $3,205,500 of 10% term corporate bonds on March 1, 2020, due on March 1, 2035, with interest payable each March 1 and September 1, with the first interest payment on September 1st, 2020. At the time of issuance, the market interest rate for similar financial instruments is 8%.

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As the controller of the company, determine the selling price of the bonds. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Selling price of the bonds

$enter the Selling price of the bonds in dollars rounded to 0 decimal places

Answer 1

1.

Compute contributed each year by Steve Fowler to provide a fund sufficient to retire the debt on March 1, 2028:

Compute the amount to be repaid including interest:

Amount of repayment including interest = Amount borrowed*(1+i)^n

=$94,900*(1.03)^20

=$94,900*1.80611

$171399.84

Annual amount to be contributed = Amount to be repaid including interest/((((1+i)^n-1)/i*(1+i))

=171399.84/((((1.05)^5-1)/0.05)*(1.05))

=171399.84/5.80191

=$29,542

The Annual contribution to debt retirement fund = $29,542

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2.

Calculation before recommendation as follows:

Present value under method 1 (Given)	$2,072,000
Compute payment under method 2 [Present value]
Annual payment × PVAF(11%, 15 years)
$283,200 × 7.190869	$2036454

Recommendation: Choose method 2 because it gives lessor present value amount.

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3.

How much should Alan Bowie deposit today in an account earning 9%, compounded annually, so that he will have enough money on hand in 3 years to pay for the overhaul:

Engine overhaul	Probability	Expected Cash Outflow
$270	10%	$27
$570	30%	$171
$720	50%	$360
$920	10%	$92
Total	$650

Amount Deposit today = PVF(6%, 6year) $\times$ $650

= 0.70496 $\times$ $650

= $458

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4.

Compute selling price of the Bond as follows:

Selling price of the Bond = Present value of Interest payment + Present value of principal

Calculate Present value of interest payment:

Present value of interest payment = ($3,205,500 $\times$ 5%) $\times$ PVAF(4%, 30 years)

= $160,275  $\times$ 17.29203

= $2,771,480

__________________________________

Calculate Present value of principal:

Present value of principal = $3205500 $\times$ 0.308318

= $988313

_______________________________

Selling price of the Bond = Present value of Interest payment + Present value of principal

= $2,771,480 + $988313

= $3759793