Solutions to HW 2 _5-8 _ 1-4 are same as for HW2a_

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```					Solutions to HW 2 #5-8 ( 1-4 are same as for HW2a)

5. L.J.'s Toys Inc. just purchased a \$200,000 machine to produce toy cars. The machine will
be fully depreciated by the straight-line method over its five-year economic life. Each toy
sells for \$25. The variable cost per toy is \$5, and the firm incurs fixed costs of \$350,000 each
year. The corporate tax rate for the company is 25 percent. The appropriate discount rate is
12 percent. What is the financial break-even point for the project?

When calculating the financial breakeven point, we express the initial investment as an
equivalent annual cost (EAC). Dividing the initial investment by the seven-year annuity
factor, discounted at 12 percent, the EAC of the initial investment is:

EAC = Initial Investment / PVIFA12%,5

EAC = \$200,000 / 3.60478

EAC = \$55,481.95

Note that this calculation solves for the annuity payment with the initial investment as the
present value of the annuity. In other words:

PVA = C({1 – [1/(1 + R)]t } / R)

\$200,000 = C{[1 – (1/1.12)5 ] / .12}

C = \$55,481.95

The annual depreciation is the cost of the equipment divided by the economic life, or:

Annual depreciation = \$200,000 / 5

Annual depreciation = \$40,000

Now we can calculate the financial breakeven point. The financial breakeven point for
this project is:

QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)]

QF = [\$55,481.95 + \$350,000(.75) – \$40,000(0.25)] / [(\$25 – 5) (.25)]

QF = 20,532.13 or about 20,532 units

6.
Ang Electronics, Inc., has developed a new DVDR. If the DVDR is successful, the present value of
the payoff (at the time the product is brought to market) is \$20 million. If the DVDR fails, the
present value of the payoff is \$5 million. If the product goes directly to market, there is a 50 percent
chance of success. Alternatively, Ang can delay the launch by one year and spend \$2 million to
test market the DVDR. Test marketing would allow the firm to improve the product and increase the
probability of success to 75 percent. The appropriate discount rate is 15 percent.
Required:

(a) Calculate the NPV

We need to calculate the NPV of the two options, go directly to market now, or utilize test
marketing first. The NPV of going directly to market now is:

NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure)

NPV = \$20,000,000(0.50) + \$5,000,000(0.50)

NPV = \$12,500,000

Now we can calculate the NPV of test marketing first. Test marketing requires a \$2
million cash outlay. Choosing the test marketing option will also delay the launch of the
product by one year. Thus, the expected payoff is delayed by one year and must be
discounted back to year 0.

NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t

NPV = –\$2,000,000 + {[\$20,000,000 (0.75)] + [\$5,000,000 (0.25)]} / 1.15

NPV = \$12,130,434.78

The company should go directly to market with the product since that option has the
highest expected payoff.

7.
We are examining a new project. We expect to sell 7,000 units per year at \$60 net cash flow
apiece for the next 10 years. In other words, the annual operating cash flow is projected to be
\$60 × 7,000 =\$420,000. The relevant discount rate is 16 percent, and the initial investment
required is \$1,800,000. Suppose you think it is likely that expected sales will be revised
upwards to 9,000 units if the first year is a success and revised downwards to 4,000 units if
the first year is not a success, which means the project will be abandoned for \$1,400,000. (Do
not include the dollar sign (\$). Round your answer to 2 decimal places. For example
3.16)

Requirement 1:

If success and failure are equally likely, what is the NPV of the project? Consider the
possibility of abandonment in answering

If we couldn't abandon the project, the present value of the future cash flows when the
quantity is 4,000 will be:

PV future CFs = \$60(4,000)(PVIFA16%,9)

PV future CFs = \$1,105,570.53

The gain from the option to abandon is the abandonment value minus the present value of the
cash flows if we cannot abandon the project, so:

Gain from option to abandon = \$1,400,000 – 1,105,570.53

Gain from option to abandon = \$294,429.47

We need to find the value of the option to abandon times the likelihood of abandonment. So,
the value of the option to abandon today is:

Option value = (.50)(\$294,429.47)/1.16

Option value = \$126,909.25

8. A firm is considering an investment in a new machine with a price of \$32 million to replace
its existing machine. The current machine has a book value of \$8 million, and a market value
of \$9 million. The new machine is expected to have a four-year life, and the old machine has
four years left in which it can be used. If the firm replaces the old machine with the new
machine, it expects to save \$5 million in operating costs each year over the next four years.
Both machines will have no salvage value in four years. If the firm purchases the new
machine, it will also need an investment of \$500,000 in net working capital. The required
return on the investment is 10 percent, and the tax rate is 39 percent.

Replacement decision analysis is the same as the analysis of two competing projects, in this
case, keep the current equipment, or purchase the new equipment. We will consider the
purchase of the new machine first

Purchase new machine:

The initial cash outlay for the new machine is the cost of the new machine, plus the increased
net working capital. So, the initial cash outlay will be:

Purchase new machine                    -\$ 32,000,000

Net working capital                           -500,000

Total                                   -\$ 32,500,000

Next, we can calculate the operating cash flow created if the company purchases the new
machine. The saved operating expense is an incremental cash flow, so using the pro forma
income statement, and adding depreciation to net income, the operating cash flow created by
purchasing the new machine each year will be:

Operating expense                          \$ 5,000,000

Depreciation                                  8,000,000
EBT                                        -\$ 3,000,000

-
Taxes                                          1,170,000

Net income                                 -\$ 1,830,000

OCF                                         \$ 6,170,000

So, the NPV of purchasing the new machine, including the recovery of the net working capital,
is:

NPV = -\$32,500,000 + \$6,170,000(PVIFA10%,4) + \$500,000 / 1.104

NPV = -\$12,600,423.47

And the IRR is:

0 = -\$32,500,000 + \$6,170,000(PVIFAIRR,4) + \$500,000 / (1 + IRR)4

Using a spreadsheet or financial calculator, we find the IRR is:

IRR = -9.38%

Now we can calculate the decision to keep the old machine:

Keep old machine:

The initial cash outlay for the new machine is the market value of the old machine, including any
potential tax. The decision to keep the old machine has an opportunity cost, namely, the
company could sell the old machine. Also, if the company sells the old machine at its current
value, it will incur taxes. Both of these cash flows need to be included in the analysis. So, the
initial cash flow of keeping the old machine will be:

Keep machine                              -\$ 9,000,000

Taxes                                          390,000

Total                                     -\$ 8,610,000

Next, we can calculate the operating cash flow created if the company keeps the old machine.
There are no incremental cash flows from keeping the old machine, but we need to account for
the cash flow effects of depreciation. The income statement, adding depreciation to net income
to calculate the operating cash flow will be:

Depreciation                                \$ 2,000,000
EBT                                        -\$ 2,000,000

Taxes                                           -780,000

Net income                                 -\$ 1,220,000

OCF                                         \$    780,000

So, the NPV of the decision to keep the old machine will be:

NPV = -\$8,610,000 + \$780,000(PVIFA10%,4)

NPV = -\$6,137,504.95

And the IRR is:

0 = -\$8,610,000 + \$780,000(PVIFAIRR,4)

Using a spreadsheet or financial calculator, we find the IRR is:

IRR = 0%

The company should purchase the new machine since it has a greater NPV.

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