# Basic present value calculations

1.

Basic present value calculations

Calculate

the present value of the following cash flows, rounding to the nearest dollar:

a. A single cash inflow of $12,000 in five years,

discounted at a 12% rate of return.

b. An annual receipt of $16,000 over the next 12

years, discounted at a 14% rate of return.

c. A single receipt of $15,000 at the end of Year

1 followed by a single receipt of $10,000 at the end of Year 3. The company has

a 10% rate of return.

d. An annual receipt of $8,000 for three years

followed by a single receipt of $10,000 at the end of Year 4. The company has a

16% rate of return.2.

Cash flow calculations and net present valueOn

January 2, 20X1, Bruce Greene invested $10,000 in the stock market and

purchased 500 shares of Heartland Development, Inc. Heartland paid cash

dividends of $2.60 per share in 20X1 and 20X2; the dividend was raised to $3.10

per share in 20X3. On December 31, 20X3, Greene sold his holdings and generated

proceeds of $13,000. Greene uses the net-present- value method and desires a

16% return on investments.a. Prepare a chronological list of the

investment’s cash flows. Note: Greene is entitled to the 20X3 dividend.b. Compute the investment’s net present value,

rounding calculations to the nearest dollar.

c. Given the results of part (b), should Greene

have acquired the Heartland stock? Briefly explain.3.

Straightforward net present value and internal rate of returnThe

City of Bedford is studying a 600-acre site on Route 356 for a new landfill.

The startup cost has been calculated as follows:Purchase

cost: $450 per acreSite

preparation: $175,000The

site can be used for 20 years before it reaches capacity. Bedford, which shares

a facility in Bath Township with other municipalities, estimates that the new

location will save $40,000 in annual operating costs.

a. Should the landfill be acquired if Bedford

desires an 8% return on its investment? Use the net-present-value method to

determine your answer.4.

Straightforward net-present-value and payback computationsSTL

Entertainment is considering the acquisition of a sight-seeing boat for summer

tours along the Mississippi River. The following information is available:Cost

of boat $500,000Service

life 10 summer seasonsDisposal

value at the end of 10 seasons $100,000Capacity

per trip 300 passengersFixed

operating costs per season (including straight-line depreciation) $160,000Variable

operating costs per trip $1,000Ticket

price $5 per passengerAll

operating costs, except depreciation, require cash outlays. On the basis of

similar operations in other parts of the country, management anticipates that

each trip will be sold out and that 120,000 passengers will be carried each

season. Ignore income taxes.Instructions:

By

using the net-present-value method, determine whether STL Entertainment should

acquire the boat. Assume a 14% desired return on all investments- round

calculations to the nearest dollar.5.

Equipment replacement decisionColumbia

Enterprises is studying the replacement of some equipment that originally cost

$74,000. The equipment is expected to provide six more years of service if

$8,700 of major repairs are performed in two years. Annual cash operating costs

total $27,200. Columbia can sell the equipment now for $36,000; the estimated

residual value in six years is $5,000.New

equipment is available that will reduce annual cash operating costs to $21,000.

The equipment costs $103,000, has a service life of six years, and has an

estimated residual value of $13,000. Company sales will total $430,000 per year

with either the existing or the new equipment. Columbia has a minimum desired

return of 12% and depreciates all equipment by the straight-line method.Instructions:

a. By using the net-present-value method,

determine whether Columbia should keep its present equipment or acquire the new

equipment. Round all calculations to the nearest dollar, and ignore income

taxes.

b. Columbia’s management feels that the time

value of money should be considered in all long-term decisions. Briefly discuss

the rationale that underlies management’s belief.