CBU FINC 5401-12-Mid-Term2-Take-Home 2023
Fall
1. Consider the following capital budgeting problem. The following two machines are mutually
exclusive and the firm would keep reinvesting in whatever machine it buys. Machine A would
be reinvested every 4 years, machine B every 3 years. The cash flows associated with each
machine are tabulated as follows; all numbers are in thousand dollars; the relevant discount
rate is 10% for both machines.
Year Machine A Machine B
0
-80
-100
1
52
60
3
52
60
4
24
–
1.a Which of the two machines is the better investment project? Analyze the question under the
assumption that whatever machine the company buys has to be reinvested in perpetuity.
1.b Suppose A fits current technology, whereas machine B needs a one-time retooling for the company.
These one-off installation costs would be $10,000 today. What is the optimal investment decision
now?
1.c Suppose the investment opportunity described above lasts only for 24 years. Recalculate your
decision rule for questions 1.a and 1.b. What is the NPV of the optimal investment policy now
2. You have recently been hired by Gold-in-Sacks, Inc. The job starts immediately and you will be
paid monthly, with a starting salary of $7,000 per month (you receive your first payment
exactly one month from today). You expect your salary to increase at the rate of 4% p.a.
throughout your career, and you plan to retire in 30 years. Specifically, in your first year of
employment you will receive 12 monthly payments of $7,000. In your second year, you will
receive 12 monthly payments of $7,280 ($7,000 x 1.04), and so on. The appropriate discount
rate is 12% per annum compounding monthly.
Compute the present value of your future income as of today.
2a. Calculate the value, as of one year from today, of the first 12 monthly payments.
2b. Using your result from a), calculate the present value of your total projected future income.