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?

Please include formulas and calculations. Thanks.

Answer 1

First 7 years, the payments are constant at 100 hence it is an ordinary annuity
Present Value=Annuity/rate*(1-1/(1+rate)^n)=100/10%*(1-1/1.1^7)=486.8418818

Value of the growing perpetuity at the end of year 9=Expected cash flow/(discount rate-growth rate)=75/(10%-9%)=7500

Present Value of the perpetuity=Amount/(1+rate)^n=7500/1.1^9=3180.732138

Total Present Value of receipts=486.8418818+3180.732138=3667.57402

Value of the service fee at the end of year 1=Constant Perpetuity=Annuity/rate=15/10%=150

Present Value of the perpetuity=Amount/(1+rate)^n=150/1.1^1=136.3636364

Total Present Value=3667.57402-136.3636364=3531.210384