Jim signed a new deal for $10 million with the Toronto maple leafs. THe terms of the contract were 1 million immediately and 800,000 per year for the next 5 years (first payment after 1 year) and $1 million per year for the next 5 years (first payment at year 6). If jim's interest rate is 8% per year, how much is his contract worth at the time of the signing?
An Excel spreadsheet is very helpful for these types of calculations.
(in thousands for brevity):
PV = 1000 + 800/(1.08) + 800/1.08)^2 + 800/(1.08)^3 + .... 1000/(1.08)^10
To determine the present value of Jim's contract at the time of signing, we need to calculate the present values of the future cash flows and add them up.
The immediate payment of $1 million does not need to be discounted since it is received immediately. Therefore, the present value of the immediate payment is $1 million.
For the next 5 years (years 1 to 5), Jim will receive $800,000 per year, with the first payment being received at the end of year 1. This is an annuity with a future value of $800,000 per year, an interest rate of 8%, and a duration of 5 years. We can use the formula for the present value of an ordinary annuity to calculate the present value of these cash flows:
PV = PMT * (1 - (1 + r)^-n) / r,
where PV is the present value, PMT is the payment per period, r is the interest rate per period (in this case, 8% or 0.08), and n is the number of periods (in this case, 5).
Using this formula, the present value of the annuity is:
PV = $800,000 * (1 - (1 + 0.08)^-5) / 0.08.
Calculating this value gives us a present value of approximately $3,097,287.83.
For the next 5 years (years 6 to 10), Jim will receive $1 million per year, with the first payment being received at the end of year 6. Again, this is an annuity with a future value of $1 million per year, an interest rate of 8%, and a duration of 5 years. Using the same formula as before, the present value of this annuity is:
PV = $1,000,000 * (1 - (1 + 0.08)^-5) / 0.08.
Calculating this value gives us a present value of approximately $3,868,702.88.
Finally, to find the total present value of Jim's contract, we add up the present values of the immediate payment, the annuity from years 1 to 5, and the annuity from years 6 to 10:
Total present value = $1 million + $3,097,288 + $3,868,703.
Calculating this gives us a total present value of approximately $7,965,991.71.
Therefore, Jim's contract is worth approximately $7,965,991.71 at the time of signing.