Final answer:
Crissie should choose the lump sum if her expected interest rate is 9%. If her expected interest rate is 8%, the best choice is the 10 end-of-year payments. Interest rates influence the optimal choice by affecting the present value of future payments.
Step-by-step explanation:
To determine which award option Crissie should choose, we need to calculate the present value of each option and compare them. The present value formula is:
PV = Payment / (1 + Interest Rate)^t
a. For the lump sum of $61 million, the present value is $61 million / (1 + 0.07)^0 = $61 million.
b. For the 10 end-of-year payments of $9.5 million, the present value is $9.5 million / (1 + 0.08)^1 + $9.5 million / (1 + 0.08)^2 + ... + $9.5 million / (1 + 0.08)^10 = $68.03 million.
c. For the 30 end-of-year payments of $5.5 million, the present value is $5.5 million / (1 + 0.09)^1 + $5.5 million / (1 + 0.09)^2 + ... + $5.5 million / (1 + 0.09)^30 = $67.74 million.
b. If Crissie expects to earn 8% annually, the best choice is to choose the 10 end-of-year payments of $9.5 million, as the present value is the highest among the three options, at $68.03 million.
c. If Crissie expects to earn 9% annually, I would recommend choosing the lump sum of $61 million, as its present value is the highest among the three options.
d. Interest rates influence the optimal choice by affecting the present value of future payments.
Higher interest rates lead to lower present values, meaning that receiving a lump sum or a smaller number of larger payments might be more beneficial.
Conversely, lower interest rates increase the present value, making more frequent smaller payments a better option.