Nancy Sly wishes to sell her business and receives the following three offers:?
1. $568,000 cash immediately.
2. $200,000 cash now plus an annual installment of $60,000 at the end of each year for 10 years, a total of $800,000.
3. An offer to manage the property for 10 years that would yield her $96,000 cash at the end of each of the 10 years. She would have to make an initial investment of $20,000 cash now. Total cash received is $940,000.
Equally risky alternatives yield 10% per year.
Which offer is the best and why. To make an good response you need to compare the present value of each offer.
To determine which offer is the best, we need to compare the present value of each offer. Present value is the value today of a future sum of money, taking into account the time value of money.
Let's calculate the present value of each offer using a 10% discount rate.
1. Offer 1: $568,000 cash immediately.
The present value of this offer is simply $568,000 since it is already in cash.
2. Offer 2: $200,000 cash now plus an annual installment of $60,000 at the end of each year for 10 years, a total of $800,000.
To calculate the present value of the annual installments, we will use the formula for the present value of an annuity: PV = P * (1 - (1 + r)^(-n)) / r, where PV is the present value, P is the annual payment, r is the discount rate, and n is the number of years.
Using this formula, the present value of the annual installments is: PV = $60,000 * (1 - (1 + 0.10)^(-10)) / 0.10 = $377,905.20.
Adding the present value of the cash received now, the total present value of Offer 2 is: $200,000 + $377,905.20 = $577,905.20.
3. Offer 3: An offer to manage the property for 10 years that would yield $96,000 cash at the end of each of the 10 years. Initial investment of $20,000 cash now. Total cash received is $940,000.
To calculate the present value of the annual cash flows, we will again use the formula for the present value of an annuity:
PV = P * (1 - (1 + r)^(-n)) / r.
Using this formula, the present value of the annual cash flows is: PV = $96,000 * (1 - (1 + 0.10)^(-10)) / 0.10 = $678,106.80.
Subtracting the initial investment, the total present value of Offer 3 is: $678,106.80 - $20,000 = $658,106.80.
Comparing the present values of the three offers, we can see that:
1. Offer 1 has a present value of $568,000.
2. Offer 2 has a present value of $577,905.20.
3. Offer 3 has a present value of $658,106.80.
Therefore, the best offer for Nancy Sly is Offer 3, as it has the highest present value among the three offers.