Question

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 fair price of the Stax is the present value of all the future cash flows which are as below :

1. Cash flows of $100 at the end of each year till 7 years

2. $ 75 at end of 10th year and each year growing at 9% forever

3. Service fee (negative cashflow) of $15 each year from end of year 2 each year forever

The PV of cashflows mentioned at 1

= 100/1.1 +100/1.1² + ... 100/1.1⁷

=100/0.1 (1-(1/1.1)⁷)

= $486.84

PV of Cashflows mentioned at 2

= 75/1.1¹⁰ + 75*1.09/1.1¹¹ + .... to infinity

This is an infinite GP and the sum is given by S = a/(1-r) (for -1<r<1)

where a is first term = 75/1.1¹⁰ and r is common ratio = 1.09/1.1 which is less than 1

So, PV = 75/1.1¹⁰ / ( 1- (1.09/1.1) )

= $ 3180.73

PV of Cashflows mentioned at 3

= - (15/1.1² + 15/1.1³ + .... to infinity)

By the same formula as above

PV = - (15/1.1² / (1 -(1/1.1)))

= - $136.36 (This is a negative cash flow as it is service fee paid, So PV is also negative)

So, the value of the Stax

= Sum of PV of all cashflows

= 486.84+3180.73-136.36

=$ 3531.21 which is the fair price of the Stax