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Hello sir, I have a question that I tried to solve for quite some time.
An investment of $100,000 to be made on 31 Dec 2017 will produce an annual return of $13,000 in perpetuity, with the first income occuring on 1 January 2018. What is the net present value of this investment (to nearest $10) on 31 December 2016, discounted at 10%?
A. $11,820
B. $25,450
C. $39,090
D. $79,090Time 0 is 31 December 2016.
The investment is made in 1 years time.
The returns also start in 1 years time.Therefore the cash flows are:
1 (100,000)
1 to infinity 13,000 p.a.You then discount both in the normal way and you will arrive at an NPV of $39,090
Have you watched my free lectures on this? The lectures are a complete free course for Paper MA and cover everything needed to be able to pass the exam well.
Hello sir, i was going through this qn.
But still dont get it.
When you say discount both in the normal way how.
For the 100,000 its on year 1 not on year 0.
So do we discount it using the simple discounting formulae of X × (1+r)^-n
and get $90909.
Then for the 13000 we discount it using the perpetuity formula which is X × (1÷r)
And get $130,000.
So we take $90909 – $130,000 = -39090.Is this how its done.
If yes, the NPV is a negative but the answer is in positive, so can u ignore the negative in this case?The NPV is not negative!!!!
The PV of the 13,000 per year is + 130,000 because they are cash inflows.
The PV of 100,000 in 1 year is – 90,909 because it is a cash outflow.Therefore the NPV is 130,000 – 90,909 = + 39,091.
Have you actually watched my free lectures on this?
Ow yes!
I guess I just confused myself at the end.
Actually I haven’t yet watched it, I better watch it right away.
Thank you so much sir John 🙂
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