Homework #2: Should We Do the Project?

RiceMSIS Econ-Finance

Due April 30Spring 2003

Homework #2: Should We Do the Project?

I. A widget manufacturer currently produces 200,000 units per year. It buys widget lids from an outside supplier at a price of $2 a lid. The plant manager believes that it would be cheaper to make these lids rather than buy them. Direct production costs are estimated to be only $1.50 a lid. The necessary machinery would cost $150,000. The investment could be written off for tax purposes using a depreciation schedule (MACRS) with the following % taken each year:

Yr 1 – 14.29%Yr 2 – 24.49%Yr 3 – 17.49%Yr 4 – 12.49%

Yr 5 – 8.93%Yr 6 – 8.93%Yr 7 – 8.93%Yr 8 – 4.45%.

The plant manager estimates that the operation would require additional working capital of $30,000 but argues that this sum can be ignored since it is recoverable at the end of the 10 years that the machine will last. If the company pays a tax rate of 35% and its opportunity cost of capital is 15%, would you support the plant manager’s proposal? State clearly any assumptions that you make.

II. UW business school graduate Brenda is moving back to Seattle, and is deciding between two alternative condominium purchases. She considers the two options equally desirable as places to live, but they have different prices and different financing terms. The Fremont condo has a price of $64,000, and the sellers have agreed to finance $54,000 of the amount with a 9 year zero interest loan-- they merely require a $10,000 down payment and 9 successive yearly payments of $6000. The Northgate condo has a price of $40,000, but this amount must be paid up front in cash. Brenda currently has $75,000 in her bank account, so she can afford the cash requirement of either purchase. Assume that her opportunity cost of capital, and therefore the effective annual rate of interest she earns on her bank account, is 10%. Assume that there are no taxes of any kind. Also assume that both condos will sell for the same price in 10 years when Brenda expects to move out.

Brenda has done her own analysis of which to buy, as represented by the spreadsheet on the following page (excel file condo). In line with her finance training, she has listed all the cash flows that will accrue to her from her bank account and home purchase, and discounted them all back to present value terms. She finds that the NPV cost of the Fremont Condominium is less than that of the Northgate one by about $5000. She is therefore prepared to buy in Fremont.

A) Critically evaluate Brenda's analysis. In the process, discuss how you would analyze such a decision. Do you think her decision to buy in Fremont makes good sense?

(II Continued)

B) Brenda's good friend Kelly tells Brenda, "You are making an error. I don't understand NPV at all, but I do see that your own analysis shows that you will have about $12000 more ($91,000 vs. $79,000) in your bank account 10 years from today if you buy in Northgate. I would forget NPV, buy in Northgate, and enjoy the extra $12000." Critically evaluate Kelly's logic and advice. Does the extra $12,000 she points to have any relation to NPV?

C) Brenda's rich cousin Sam says to Brenda, "It is silly to get involved in fancy financing terms like those in Fremont. You should just buy the condo with the lower price and let me loan you the money for your purchase at standard market rates. Then you can have regular MONTHLY mortgage payments of reasonable size like everyone else."

1. Critically evaluate Sam's advice.

2. What would Brenda's monthly mortgage payment be if she followed Sam's advice?

A / B / C / D / E / F / G / H
Time / Beginning / House / Interest / Columns / PV of / PV of / Overall
balance on / Payment / inflow / B plus D / House / Interest / NPV of
this date / on this / over NEXT / minus / Payment / Inflow / All Cash
[E of row / date / year / Column C / Flows
prior] / .10(B-C) / B+D-C / F+G
Northgate Condominium Analysis
0 / 75000.00 / 40000.00 / 3500.00 / 38500.00 / -40000.00 / 3181.82
1 / 38500.00 / 0.00 / 3850.00 / 42350.00 / 0.00 / 3181.82
2 / 42350.00 / 0.00 / 4235.00 / 46585.00 / 0.00 / 3181.82
3 / 46585.00 / 0.00 / 4658.50 / 51243.50 / 0.00 / 3181.82
4 / 51243.50 / 0.00 / 5124.35 / 56367.85 / 0.00 / 3181.82
5 / 56367.85 / 0.00 / 5636.79 / 62004.64 / 0.00 / 3181.82
6 / 62004.64 / 0.00 / 6200.46 / 68205.10 / 0.00 / 3181.82
7 / 68205.10 / 0.00 / 6820.51 / 75025.61 / 0.00 / 3181.82
8 / 75025.61 / 0.00 / 7502.56 / 82528.17 / 0.00 / 3181.82
9 / 82528.17 / 0.00 / 8252.82 / 90780.99 / 0.00 / 3181.82
10 / 90780.99
Sum / -40000.00 / 31818.18
NPV at 10% / -8181.82
Fremont Condominium Analysis
0 / 75000.00 / 10000.00 / 6500.00 / 71500.00 / -10000.00 / 5909.09
1 / 71500.00 / 6000.00 / 6550.00 / 72050.00 / -5454.55 / 5413.22
2 / 72050.00 / 6000.00 / 6605.00 / 72655.00 / -4958.68 / 4962.43
3 / 72655.00 / 6000.00 / 6665.50 / 73320.50 / -4507.89 / 4552.63
4 / 73320.50 / 6000.00 / 6732.05 / 74052.55 / -4098.08 / 4180.07
5 / 74052.55 / 6000.00 / 6805.26 / 74857.81 / -3725.53 / 3841.39
6 / 74857.81 / 6000.00 / 6885.78 / 75743.59 / -3386.84 / 3533.49
7 / 75743.59 / 6000.00 / 6974.36 / 76717.94 / -3078.95 / 3253.59
8 / 76717.94 / 6000.00 / 7071.79 / 77789.74 / -2799.04 / 2999.13
9 / 77789.74 / 6000.00 / 7178.97 / 78968.71 / -2544.59 / 2767.81
10 / 78968.71
Sum / -44554.14 / 41412.86
NPV at 10% / -3141.29