1. Consider the following two projects Project A: Costs $10,000 today. Increases
ID: 1181347 • Letter: 1
Question
1. Consider the following two projects
Project A: Costs $10,000 today. Increases profit by $4000 next year and $7,200 the year after that
Project B: Costs $6000 today. Increases profit in two years by $6678
A firm faces a rate to borrow money of 8% and has the option of investing money with almost no risk at 6%.
a) If the firm has $20,000 on hand, with only these two project to choose from, will they invest in A, B, neither or both? Show the calculations that lead to your conclusions. Explain whether you answers would be different for either project if the firm had no money on hand to invest. (2 points)
Explanation / Answer
1. a.
case 1, neither:
y0: 20,000
y1: y0*1.06 = 21,200
y2: y1*1.06 = 22,472
case 2, A:
y0: 10,000
y1: y0*1.06 + 4,000 = 14,600
y2: y1*1.06 + 7,200 = 22,676
case 3, B:
y0: 14,000
y1: y0*1.06 = 14,840
y2: y1*1.06 + 6,678 = 22,408.40
case 4, A&B:
y0: 4,000
y1: y0*1.06 + 4,000 = 8,240
y2: y1*1.06 + 7,200 + 6,678 = 22,612.4
The firm would invest in A since the return after two years is the greatest.
If the firm had no money on hand and had to borrow to invest, the formulas would remain largely untouched, substituting 1.08 for 1.06 because the interest is higher on lending. y0 would also be negative values representing how much was borrowed to invest. In this case, project A would no longer be economically advantageous, since the increased profit would not cover the interest payments. So if the firm had no cash on hand it would not invest in either project.
b.
10,000*(x^2) = 4,000 *x + 7,200
c.
It was worth investing in A when we were giving up 6% risk free rate, therefore the rate of return of A is higher than 6%.
Conversely, it wasn't worth investing when the rate was 8%, therefore the rate of return of A is lower than 8%. These two facts imply the rate of return of A is between 6% and 8%.
d.
The bound is an upper bound of 6% since project B is still advantageous even when we have to borrow at that rate to finance it. There is a lower bound of 0% since we are not losing money.
6,000*(x^2) = 6678 => x = 1.055 => 5.5%
Which fits in the predicted bounds
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