Question

1. A financial engineer designs a new financial instrument that he calls, the Stax. This instrument gives the holder access to the following cashflows: • For the first 7 years, the holder receives $100 per year starting one year from today (a total of 7 payments) • The holder does not receive any cashflows for years 8 or 9 • Starting at the end of year 10, the holder receives $75 growing at a rate of 9% per year forever The holder has to pay a "service fee" of $15 every year starting at the end of year 2; this goes on forever The prevailing discount rate throughout is 10%. The financial engineer would like to determine a fair market price for this financial instrument, what do you suggest this price to be? (8 marks)

Answer 1

The cashflow for the given instrument is below. NPV is also given. Explanation is after the casfhlow.

Year	Cashflow
1	100
2	-50
3	100
4	100
5	100
6	100
7	100
8	0
9	0
10	7500
NPV	3254

The holder receives 100 for first 7 years, that is straight forward. The issue is that he also has to pay 15 starting year 2 onwards. This is a negative cashflow and goes on till perpetuity. We know that, for a cashflow going on till perpetuity,

NPV=1/discount rate. So, for $15 in perpetuity at 10% discount rate

NPV=-15/.1=-150. Hence we can just say that at year 2 there is a -150 cashflow. Hence net cashflow in year 2= 100-150=-50.

The second issue is of $75 payments increasing by 9% per year till perpetuity.  We also know that for growting perpetuity cashflows

NPV=Initial amount/(discount rate-growth rate). So, in our case

NPV of 75 increasing at 9%=75/(.1-.9)=75/.01=7500. This is shown at year 10 as it starts there.

Now we have final cashflow. All we need to do is to calculate its NPV and that will be the fair value. Using excel formula =NPV(rate,cashflow), we get the NPV. We can also calculate it manually with the following formula

=cashflow1/(1+r)+cashflow2/(1+r)²+......+cashflown/(1+r)ⁿ

Hence, the fair value is 3254