TIME VALUE OF MONEY

$1.$ Don Juan invested $$10,000$ today in a fund that earns $8\%$ compounded annually.

To what amount will the investment grow in $3$ years?

$2.$ Marty Hardy will invest $$5,000$ a year for $20$ years in a fund that will earn $10\%$ annual interest. If

the first payment into the fund occurs today, what amount will be in the fund in $20$ years?

$3.$ Joe Schmoe needs $$20,000$ in $4$ years. What amount must he invest today if his investment

earns $10\%$ compounded annually?

$4.$ Arabella Narcissus is investing for the future. She is looking at two options. Calculate the

amounts for each scenario.

a$)$ Arabella can invest $$22,000$ today at $8\%.$ How much cash will she have for at the end of

twenty years?

b$)$ Arabella can invest $$1,000$ each year for twenty years at $6\%$ interest. What will be the

value of her investment at the end of twenty years?

NET PRESENT VALUE, PAYBACK PERIOD, & UNADJUSTED RATE OF RETURN

Maleficent produces Beauty Sleep, a powerful sleep aide. The company is considering using a patented

manufacturing process which it expects to cut production costs considerably. The license fee for the

process will be a one$-$time fee of $$25,000$ before the process is implemented and then an annual renewal

fee of $$3,000($note: this license renewal fee would begin at the end of Year $1$ and the last payment would

be made at the end of Year $9.$ The project is over at the end of Year $10.)$ The company believes that it

will save $$9,000$ per year for the next ten years. After the fourth year some retraining will occur at a cost

of $$5,000$ and again after the eighth year for an estimated $$7,000.$ Assume depreciation is an average of

$$3,200$ per year. Also, some of the company$$s existing machinery will be sold for $$7,000.$ The company

expects the sale to take place after two years when it has had time to find a buyer. Assume that the

company prefers to have a payback period of $2$ years or less and an unadjusted rate of return of at least

$8\mathrm{.}5\%.$

$1.$ What is the net present value of this project?

$2.$ Based on the net present value assessment only, should the company invest in this machine?

$3.$ What is the payback period of this machine?

$4.$ Based on the payback period only, should the company buy the machine?

$5.$ What is the unadjusted rate of return of this machine?

$6.$ Based on the unadjusted rate of return only, should the company buy the machine?

BONDS

Counting Crows Corp. issues $5-$year $12\%$ bonds with a $$200,000$ face value. The bonds are to be

compounded quarterly. On the bond issue date the effective interest rate $($market rate$)$ of similar bonds is

$20\%($this company is high$-$risk$).$

a$.$ Calculate the value of the bonds.

b$.$ Determine the amount of any premium or discount on the bonds.

VARIANCES

$1.$ LIFT Elevator Company manufactures small hydroelectric elevators. One of the direct materials

used is heavy$-$duty carpeting for the floor of the elevator. The direct materials quantity standard

for May was $6$ square yards per elevator. During May, the purchasing agent purchased this

carpeting at $$24$ per square yard; the standard price for the period was $$22.$ Fifty elevators were

completed and sold during the month; the Production Department used total of $290$ square yards

of carpet in May. Calculate the company$$s direct materials price and quantity variances for

carpeting for May.

$2.$ For the past two years, NE Company$$s best$-$selling product has been a titanium engine block.

Standard direct labor hours per block are $2\mathrm{.}0$ hours. The standard pay rate for direct labor

employees is $$24$ per hour. During July, NE produced $16,000$ blocks. Actual direct labor hours

and costs for the month were $31,000$ hours and $$775,000,$ respectively.

SOLUTIONS

TIME VALUE OF MONEY

IN$-$CLASS PROBLEM

$1.$ Don Juan invested $$10,000$ today in a

fund that earns $8\%$ compounded

annually. To what amount will the

investment grow in $3$ years?

$2.$ Marty Hardy will invest $$5,000$ a year

for $20$ years in a fund that will earn $10\%$

annual interest. If the first payment into

the fund occurs today, what amount will

be in the fund in $20$ years?

$3.$ Joe Schmoe needs $$20,000$ in $4$ years.

What amount must he invest today if his

investment earns $10\%$ compounded

annually?

$4.$ Arabella Narcissus is investing for the

future. She is looking at two options.

Calculate the amounts for each scenario.

a$)$ Arabella can invest $$22,000$ today

at $8\%.$ How much cash will she

have at the end of twenty years?

b$)$ Arabella can invest $$1,000$ each

year for twenty years at $6\%$

interest. What will be the value of

her investment at the end of twenty

years?

Future Value Single Sum

Investment $10,000$

Rate $1\mathrm{.}25971$

Result $12,597$

Future Value Annuity

Investment $5,000$

Rate $57\mathrm{.}27500$

Result $286,375$

Present Value Single Sum

Investment $20,000$

Rate $0\mathrm{.}68301$

Result $13,660$

Future Value Single Sum

Investment $22,000$

Rate $4\mathrm{.}66096$

Result $102,541$

Future Value Single Sum

Investment $1,000$

Rate $36\mathrm{.}78559$

Result $36,786$

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NET PRESENT VALUE, PAYBACK PERIOD, & UNADJUSTED R