An investment with an initial cost of £15,000 produces cash ﬂows of £5,000 annually for 5 years.If the cash ﬂow is evenly spread out over the year and the ﬁrm can borrow at 10%, the discounted
Payback period is _____ years.
A)3
B)3.2
C)3.75
D)4
E)5

Question

Quizplus · Accepted Answer

To calculate the discounted Payback period, we need to find out the present value of each cash flow and accumulate them until we get the initial investment back. If we use a 10% discount rate, we can discount each cash flow as follows:

Year 1: £5,000 / (1 + 0.1) ^ 1 = £4,545
Year 2: £5,000 / (1 + 0.1) ^ 2 = £4,132
Year 3: £5,000 / (1 + 0.1) ^ 3 = £3,756
Year 4: £5,000 / (1 + 0.1) ^ 4 = £3,413
Year 5: £5,000 / (1 + 0.1) ^ 5 = £3,098

Now, we can accumulate the discounted cash flows until we reach the initial investment of £15,000:

Year 1: £4,545 -> Cumulative: £4,545
Year 2: £4,132 -> Cumulative: £8,677
Year 3: £3,756 -> Cumulative: £12,433
Year 4: £3,413 -> Cumulative: £15,846
Year 5: £3,098 -> Cumulative: £18,944 (we have exceeded the initial investment)

Therefore, we can see that the discounted Payback period is between Year 4 and Year 5. To get the exact year, we need to do a linear interpolation:

Year 4 + (£15,000 - £15,846) / (£18,944 - £15,846) * 1 = 3.75

Thus, the answer is C, 3.75 years.

An Investment with an Initial Cost of £15,000 Produces Cash