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Calculating Worth of a contract and Perpetuity

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The Publicity agents for the Winterpeg Blue Strikers announce the signing of a quarterback, Shane Doe. They say that the contract is worth CAD 1 million and will be paid in 20 installments of $50000 per year starting one year from now and with one new installment each year for the next twenty years. The contract contains a clause that guarantees he will get all the money even if he is injured and cannot play a single game. Sports writers declare that Shane has become an "instant millionaire".
a.Shane's half sister Xian who majored in economics explains to Shane that he is not a millionaire, and his contract is worth less than half a million dollars. Explain why this may be so.
b.Suppose interest rate is 10% and is expected to remain 10% forever. How much would it cost the team for buy Shane a perpetuity that would pay him $20000 per year forever starting from year 1?
c.How much would it cost to buy a perpetuity of $50000?

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Solution Summary

The solution describes the steps for calculating worth of a contract. It also explains the steps to calculate that worth of a perpetuity.

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Solution

a)For any periodic payment received, there is an opportunity cost involved. The value of contract will be equal to present value of ordinary annuity with
Annual Payment=R=$50000
Number of payments=n=20

For interest rate =1%,
PV factor =(1-1/1.01^20)/0.01=18.0456
PV of ordinary ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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