Project A and B have 4 year timelines. Project A has an initial investment of $100,000 and cash inﬂows of $60,000, $50,000 $40,000 and $40,000. Project B has an initial investment of $75,000
And cash inﬂows of $50,000, $40,000, $30,000 and $30,000. At what rate of interest would a
Company be indifferent at choosing project A or B?
A) 17.95%
B) 19.01%
C) 21.86%
D) 23.88%
E) 24.44%

Question

Quizplus · Accepted Answer

To find the rate of interest at which the company is indifferent between projects A and B, we need to calculate the present value of both projects and then equate them:

PV(A) = -$100,000 + $60,000/(1+r) + $50,000/(1+r)^2 + $40,000/(1+r)^3 + $40,000/(1+r)^4
PV(B) = -$75,000 + $50,000/(1+r) + $40,000/(1+r)^2 + $30,000/(1+r)^3 + $30,000/(1+r)^4

Now we need to solve for r:

PV(A) = PV(B)
-$100,000 + $60,000/(1+r) + $50,000/(1+r)^2 + $40,000/(1+r)^3 + $40,000/(1+r)^4 = -$75,000 + $50,000/(1+r) + $40,000/(1+r)^2 + $30,000/(1+r)^3 + $30,000/(1+r)^4

By trial and error or using a financial calculator, we can find that the rate of interest that satisfies the above equation is approximately 21.86%. Therefore, the company would be indifferent at choosing project A or B if the rate of interest is 21.86% or higher.

Since project A has a higher initial investment and cash inflows, it will have a higher net present value (NPV) than project B at any interest rate lower than 21.86%. Therefore, choosing project A would be the better choice if the interest rate is lower than 21.86%. However, if the interest rate is higher than 21.86%, choosing project B would be the better choice as it has a higher NPV at that rate.

Project a and B Have 4 Year Timelines