Billy Wilson, All American
Case 11
Time Value of Money
Purpose: The case provides the student with an interesting opportunity to examine the time value of
money. Pro football contractual issues are frequently in the news so the student will be dealing with a
contemporary situation. The student also will become familiar with deferred annuity payments.
Relation to Text: The case should follow Chapter 9.
Complexity: The case is moderately complex. It should require 1 hour.
Solutions
1.
Contract offer number one
• Immediate signing bonus ………………………………………………………………………..
$ 900,000
• $850,000 at the end of each year for the next five years
PVA = A x PVIFA (n = 4, i = 10%) (Ap.D)*
PVA = $850,000 x 3.791 = ……………………………………………………………………..
3,222,350
Total present value ………………………………………………………………………………..
$4,122,350
*indicates appendix designation
Contract offer number two
• Immediate signing bonus ………………………………………………………………………..
200,000
$100,000 at the end of each year for four years
PVA = A x PVIFA (n = 4, i = 10%) (Ap.D)
PVA = $100,000 x 3.170 = ……………………………………………………………………..
+317,000
• $150,000 at the end of years five through 10)
Step 1
PVA = A x PVIFA (n = 6, i = 10%) (Ap.D)
PVA = $150,000 x 4.355 = $653,250
Step 2
PV = FV x PVIF (n = 4, i = 10%) (Ap.B)
PV = $653,250 x .683 ……………………………………………………….……………………
+446,170
• $1,000,000 a year at the end of years 11 through 40
Step 1
PVA = A x PVIFA (n = 30, i = 10%) (Ap.D)
PVA = $1,000,000 x 9.427 = $9,427,000
Step 2
PV = FV x PVIF (n = 10, i = 10%) (Ap.B)
PV = $9,427,000 x .386 …………………………..……………………………………………..
+3,638,822
Total present value ………………………………………………………………………………..
$4,601,992
Contract offer number three
• Immediate signing bonus ………………………………………………………………………..
1,000,000
• $500,000 at the end of year one
PV = FV x PVIF (n = 1, i = 10%) (Ap.B)
PV = $500,000 x .909 …………………………………………………………………………..
+454,500
• $1,000,000 at the end of year two
PV = FV x PVIF (n = 2, i = 10%) (Ap.B)
PV = $1,000,000 x .826 ………………………………………………………………………..
+826,000
• $1,500,000 at the end of year three
PV = FV x PVIF (n = 3, i = 10%) (Ap.B)
PV = $1,500,000 x .751 ………………………………………………………………………..
+1,126,500
• $2,500,000 at the end of year four
PV = FV x PVIF (n = 4, i = 10%) (Ap.B)
PV = $2,500,000 x .683 ………………………………………………………………………..
+1,707,500
• Bonus for Pro Bowl
$200,000 x .25 = $50,000 expected value per year
PV = A x PVIFA (n = 4, i = 10%) (Ap.D)
PVA = $50,000 x 3.170 ………………………………………………………………………….
+158,500
Total present value …………………………………………………………………………….
$5,273,000
2.
Contract offer by the Canadian football team
• Immediate signing bonus ………………………………………………………………………..
1,100,000
• $2,000,000 at the end of each year for three years
x .80 probability the amount will be paid
$1,600,000 expected value of the payment
PVA = A x PVIFA (n = 3, i = 10%) (Ap.D)
PVA = $1,600,000 x 2.487 ………………………………………………………………………
3,979,200
Total present value
$5,079,200
4. The second contract proposal from the U.S. team with the late cash flows would become
5.
Third contract proposal from the U.S. team
Remaining value after the agent’s 10 percent fee
Aftertax value
7. The value of an annuity:
A
=
PVA
(n = 40, i = 10%) (Ap.D)
PVIFA
A
=
$5,273,000
= $539,217
9.779
8. Answers might include:
• Possible extra revenues from commercials, personal appearances