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A project has an initial cash outflow of $12,000 followed by six equal annual cash inflows, commencing in one year’s time. The payback period is exactly four years. The cost of capital is 12% per year.
What is the project’s net present value (to the nearest $)?
A $333
B –$2,899
C –$3,778
D –$5,926The correct answer is A.
A four year payback period implies an (equal) annual cashflow of $12,000 ÷ 4 years = $3,000 per year. As these cash flows run for 6 years the NPV is equal to $333 (-$12,000 + Annuity factor for 6 years @ 12% x $3,000 = -$12,000 + 4.111 x $3,000 = $333). Alternative C is based upon an incorrect calculation of annual cashflow ($12,000 ÷ 6 years = $2,000 per year), suggesting a misunderstanding of the payback method.
My answer:
Using the Present Value Table I got a NPV of 336.
Year
(12000)
2679
2391
2136
1908
1701
1521Total 336.
I already revised all the calculations so must be a different way of doing it?
Thank you!
You were correct in writing that the cash flow will be 3,000 a year for 6 years.
To get the present value of 3,000 a year for 6 years, you need to multiply by the annuity discount factor for 6 years at 12%.
For the NPV you simply subtract from this the initial outflow of 12,000.
The reason that your answer is slightly different is simply due to the fact that the discount factors in the tables are rounded to three decimal places. Do not worry about this 🙂 The real exam will ask for figures to the nearest $100 or sometimes to the nearest $1000, so that the rounding does not present a problem.
(You might find it useful to watch the free lectures on this.)
Project L costs $65,000, its expected cash inflows are $12,000 per year for 9 years, and
its WACC is 9%. What is the project’s NPV?
Kindly help me in tackling this problem..I really do think that you need to watch our free lectures on this!!
Multiply the 12,000 by the 9 year annuity factor at 9% and then subtract the initial 95,000 so as to arrive at the net present value.
Hi Mr. John,
Can you please explain the first question asked (from Barbara).
I have watched your lectures but i cannot seem to answer this question. Please explain this to me step b step if you can.
Thank you in advance!
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