Saint Mary's is offered a contract, which offers a net present value of $15 000 if the required rate of return is 12%. Alternatively, net present value is -$12 000 if the required rate of return is 18%. At what rate of return, would the NPV be zero?
A) 13%
B) 13.7%
C) 14%
D) 14.5%
E) 15%

Question

Quizplus · Accepted Answer

To find the rate of return that would result in a zero NPV, we need to use the formula:

NPV = -initial investment + cash flows / (1 + r)^t

where r is the required rate of return and t is the time period.

Setting the NPV to zero, we can solve for r:

0 = -$15,000 + cash flows / (1 + r)^t

$15,000 = cash flows / (1 + r)^t

We can plug in the values given in the problem and solve for r:

$15,000 = -$12,000 / (1 + 0.18)^t
(1 + 0.18)^t = 1.25

t x log(1.18) = log(1.25)
t = log(1.25) / log(1.18)
t ≈ 2.78 years

$15,000 = cash flows / (1 + r)^(2.78)
(1 + r)^(2.78) = cash flows / $15,000
1 + r = (cash flows / $15,000)^(1/2.78)
r = (cash flows / $15,000)^(1/2.78) - 1

Using the first option, we get:

r = ($15,000 / $15,000)^(1/2.78) - 1 = 0%

Using the second option, we get:

r = ($12,000 / $15,000)^(1/2.78) - 1 ≈ 13.7%

Therefore, the answer is B) 13.7%.

Saint Mary's Is Offered a Contract, Which Offers a Net