Final answer:
After discounting the future repair costs to their present value with a cost of capital of 7%, PMI's total costs for the big-screen TVs extended warranty are less than the revenue from the upfront payment. Therefore, it should be a profitable endeavor for PMI to offer this warranty.
Step-by-step explanation:
To determine if Peace of Mind, Inc. (PMI) should offer the extended warranty for big-screen TVs, we need to evaluate the present value of the cash flows associated with the warranty service. PMI will receive $210 upfront and incur an average cost of $106 for repairs each year for two years. To calculate if this is financially viable, we consider the company's cost of capital at 7%.
The total repair costs over two years will be $106 + $106 = $212. These future costs need to be discounted to their present value (PV). The formula for the present value of a future cash flow is PV = C / (1 + r)^t where C is the cash flow, r is the cost of capital, and t is the time period.
For the first-year repair cost, t is 1, so PV = $106 / (1 + 0.07)¹ = $99.07. For the second-year cost, t is 2, so PV = $106 / (1 + 0.07)² = $92.61. The total PV of the two years of repair costs is $99.07 + $92.61 = $191.68.
As the present value of the costs ($191.68) is less than the upfront payment received ($210), PMI would have a positive net present value (NPV) by offering this warranty, indicating a profitable decision assuming these expected costs are accurate and all other factors remain constant.