# Sample

**Topics:**Net present value, Depreciation, Inflation

**Pages:**25 (4643 words)

**Published:**September 12, 2013

Making Investment Decisions with

the Net Present Value Rule

Answers to Problem Sets

1. a, b, d, g, h; c is a sunk cost. e is an overhead cost. f is not an incremental cash flow because depreciation is not a cash flow. i is a sunk cost.

Est. Time: 01 - 05

2.Real cash flow = 100,000/1.04 = $96,154.

The real discount rate is calculated as 1 + nominal rate / 1+ inflation rate − 1. Therefore, 1.08/1.04 − 1 = .03846.

PV = [pic]

Est. Time: 01 - 05

3.a. False. A project’s annual tax shield is equal to the depreciation amount times the tax rate.

b. False. Financing and investment decisions are kept separate.

c. False. One set of books is kept for stockholders using straight-line depreciation. Another set of books is kept for tax purposes using accelerated depreciation.

d. False. Depreciation does not affect cash flows; rather, it affects taxable income.

Est. Time: 01 - 05

4.The longer the recovery period, the less the present value of depreciation tax shields. This is true regardless of the discount rate.

First, calculate the PV for the depreciation schedules as shown below: |5-Year Schedule | | | | | | | | |Year |1 |2 |3 |4 |5 |6 | | |Year |1 |2 |3 |4 |5 | |Working Capital |50,000 |230,000 |305,000 |250,000 |0 | |Cash Flows |+50,000 |+180,00 |+75,000 |−55,000 |−250,000 |

5.

Working capital = inventory + accounts receivable – accounts payable. Cash flows = change in working capital.

Est. Time: 01 - 05

6.Comparing present values can be misleading when projects have different economic lives and the projects are part of an ongoing business. For example, a machine that costs $100,000 per year to buy and lasts five years is not necessarily more expensive than a machine that costs $75,000 per year to buy but lasts only three years. Calculating the machines’ equivalent annual costs allows an unbiased comparison. Est. Time: 01 - 05

7.First calculate the PV of the costs of the system for 25 years. This equals $4,318,788.91. Next, calculate the 25-year annuity factor. The annuity factor for 25 years at 5% is 14.09. To calculate the equivalent annual cost, divide the PV by the 25-year annuity factor: $4,318,788.91/14.09 = $306,514.

Est. Time: 01 - 05

8.a.NPVA = $100,000; NPVB = $180,000.

b.Given the NPV for each project, we need to find the annuity factors. Project A has a two-year annuity factor of 1.736. Project B has a three-year annuity factor of 2.487. Therefore:

Equivalent annual cash flow of A = 100,000/1.736 $57,604 Equivalent cash flow of B = 180,000/2.487 = $72,376

c.Machine B

Est. Time: 01 - 05

9.In this problem, we must ignore the sunk costs and past real cash flows and focus on future cash flows. Since Machine C is expected to last another five years and produces a real annual cash flow of $80,000 and Machine B’s real annual cash flow is $72,346, the company should wait and replace Machine C at the end of five years ($80,000 > $72,346).

Est. Time: 01 - 05

10.See the table below. We begin with the cash flows given in the text, Table 6.6, line 8, and use the following relationship from Chapter 3:

Real cash flow = nominal cash flow/(1 + inflation rate)t Here, the nominal rate is 20%, the expected inflation rate is 10%, and the real rate is given by the following:

|(1 + rnominal) | = (1 +...

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