W07 Case Study-Advanced TVM- Rita Rodriguez
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Case 5: TIME VALUE OF MONEY
Tom Jackson, Settlement Alternatives
:
Tom Jackson was an employee of a large farm machinery manufacturing plant located in Akron,
Ohio. He had been recently promoted and was considered by his peers to be a very good
employee. Tom’s new job involved operating a hydraulic press which was used to bend sheet
metal for tractor body panels. Tom had received minimal training prior to beginning his new
assignment. The safety instructions that were normally posted next to his hydraulic press had
been taken down prior to his taking over so that the wall could be steam cleaned. The sign
posting the safety instructions was never replaced.
Tom asked his supervisor on two separate occasions for some help in understanding some of the
finer points of running his machine, but his supervisor failed to respond. On October 27
th
, 2000,
Tom’s hand was severely injured while operating the hydraulic press. Tom was injured because
he mistakenly pressed a key that engaged the press while he was steadying a body panel with his
hand. His left hand was so badly damaged by the hydraulic press that what remained of the hand
had to be amputated after several days. Tom’s injury required hours of rehabilitation and has
created a permanent disability (especially for someone in his line of work).
Tom believed he was injured because the company negligently withheld proper training for the
machine, removed the safety instructions, and denied his repeated requests for help. Tom’s union
representative helped him acquire legal help to work out a long-term solution for compensating
him for damages due to the company’s negligence. The company knew it had a poorly defensible
case and offered to settle out of court. The company offered Tom three different settlement
alternatives (any of which Tom could choose). Had he not been injured, Tom estimated that he
would have worked an additional 22 years, before retirement. Tom’s current salary is $50,000
per year. Tom now was faced with the task of deciding which alternative would be best for him
to agree to.
The settlement alternatives:
Alternative 1:
Tom would be paid $300,000 upfront and would also receive the equivalent of
his annual pay once each year for the remainder of his estimated working years (22 payments).
Alternative 2:
Tom would receive a one-time lump-sum payment today of $750,000.
Alternative 3:
Tom would receive 22 annual payments equal to half his annual salary. At the
end of year 22, Tom would receive an additional payment of $1,000,000.
Solve:
1. Assume that a discount rate of eight percent is used, which alternative has the highest
present value? Alternatives 1 and 3 may need to be calculated in two separate parts,
adding the two answers together to get the total present value for each.
Alternative 1:
Converting the cashflows into Present Value terms
Year 0 = $300,000 x 1 + $ 50,000 x PVAF (8%,22 years) = $ 300,000 + $50,000 x 10.200744 =
$300,000.00 + $510,037.20 = $ 810,037.20
The present value of Future Annual payments is $ 510,037.20.
The present Value of the Upfront Settlement is $ 300,000.00
The combined value of Alternative 1 is $810,037.20
Alternative 2:
$750,000 received today i.e., the Current value of Alternative 2 is $750,000
Alternative 3:
Annual payment equal to Half his Annual Salary $50,000 x 50% = $25,000
Final settlement of $10,00,000 at the end of Year 22
Year 0 = $25,000 x PVAF (8%,22 years) + $1,000,000 x PVF (8%,22 years)
Year 0 = $25,000 x 10.200744 + $1,000,000 x 0.183941
Year 0 = $ 255,018.60 + $ 183,941.00 = $438,959.60
Present Value of Annual payments half his Annual Salary $ $ 255,018.60
Present Value of Final Settlement of $10,00,000 at the end of Year 22 $ 183,941.00
Present Value of Alternate 3 is $438,959.60
Therefore, it is suggested that alternate 1 has the highest Present value and is to be chosen.
2. Assume a discount rate of 11 percent (the S&P average over time...).
Does this change
the picture at all? What is the present value of each alternative now?
Alternative 1:
Converting the cashflows into Present Value terms
Year 0 = $300,000 x 1 + $ 50,000 x PVAF (11%,22 years) = $ 300,000 + $50,000 x 8.175739 =
$300,000.00 + $408,786.95 = $ 708,786.95
The present value of Future Annual payments is $ 408,786.95.
The present value of Upfront Settlement is $ 300,000.00
The combined value of Alternative 1 is $708,786.95
Alternative 2:
$750,000 was received today and the Current value of Alternative 2 is $7,50,000
Alternative 3:
Annual payment equal to Half his Annual Salary $50,000 x 50% = $25,000
Final settlement of $1,000,000 at the end of Year 22
Year 0 = $25,000 x PVAF (11%,22 years) + $1,000,000 x PVF (11%,22 years)
Year 0 = $25,000 x 8.175739 + $1,000,000 x 0.100669
Year 0 = $ 204,393.48 + $ 100,669.00 = $305,062.48
Present Value of Annual payments half his Annual Salary $ $ 2,55,018.60
Present Value of Final Settlement of $10,00,000 at the end of Year 22 $ 1,83,941.00
Present Value of Alternate 3 is $438,959.60
Therefore, it is suggested that alternate 2 has the highest Present value and is to be chosen.
3. If the insurance company becomes insolvent after the first 10 years, what would be the
present value of the cash flows collected through year 10 (use an eight percent discount
rate)?
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Alternative 1:
Present value of $300,000 + $50,000 for 10 years discounted at 8% = 300,000 + 50,000 * 6.71 =
$635,504
Alternative 2:
Present value of $750,000 = $750,000
Alternative 3:
Present value of $25,000 for 10 years discounted at 8% =25000 * 6.71 = $167,752
4.
Can you think of an alternative that Tom might propose back to the company that
would not exceed the total dollars they pay out under either alternative 1 or 3, but that
might result in a higher present value than any of the three alternatives (assuming the
eight percent discount rate)? Describe your new alternative and calculate its present value.
Total dollars paid out under alternative 1 (without time value of money) = 300,000 + 50,000 *
22 = $1,400,000
Total dollars paid out under alternative 3 (without time value of money) = 25,000 * 22 +
1,000,000 = $1,550,000
When the time value of money is considered, earlier payouts are always better because the
discounting does not come into play/ has a smaller effect. In the given scenario, if the company
is willing to pay out up to $1,550,000 in absolute dollar terms, it would be better to ask for the
entire amount upfront and avoid the discounting due to time. As there is no discounting now, the
present value of the payout would also be $1,550,000 which would be the maximum payout he
can receive.