Question

Mom and Pop Groceries has just dispatched a year's supply of groceries to the government of the Central Antarctic Republic. Payment of $250,000 will be made one year hence after the shipment arrives by snow train. Unfortunately, there is a good chance of a coup d'état in which case the new government will not pay. Mom and Pop's controller therefore decides to discount the payment at 40% rather than at the company's 12% cost of capital. a. Is it proper to use 40% as the discount rate in this situation? No Yes b. How much is the $250,000 payment really worth if the odds of a coup d'état are 25% ? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Using a 40% discount rate reflects the high risk of a political coup and non-payment. Calculating the present value, considering a 25% chance of a coup, results in the $250,000 being worth $133,928.57 today when discounted at the 40% rate.

Step-by-step explanation:

The question at hand deals with a situation where Mom and Pop Groceries has to decide on an appropriate discount rate for the expected payment from the Central Antarctic Republic, considering there is a risk of non-payment due to a coup d'état. To answer the first part of the question, using a 40% discount rate can be justifiable because it reflects the high risk of not receiving the payment if the political situation destabilizes. The second part involves calculating the present value of the future payment considering a 25% chance of a coup occurring. This type of calculation typically requires not only the discount rate but also the probabilities of the possible outcomes.

To answer the second part: if the risk of non-payment is 25%, then there is a 75% chance of receiving the payment. The present value (PV) can be calculated as follows:

• PV (payment is made) = Future Value / (1 + discount rate) = $250,000 / (1 + 0.40) = $178,571.43
• Expected PV = Probability (payment is made) * PV (payment is made) = 75% * $178,571.43 = $133,928.57 (rounded to two decimal places)

Therefore, the payment of $250,000 in a year, with a 25% risk of a coup, is worth $133,928.57 today when discounted at 40%.

Answer 2

Using a 40% discount rate may be justified if it accurately reflects the risk; however, typically, the expected payment is adjusted for probability rather than changing the discount rate. The present value of the expected $250,000 payment, with a 25% chance of a coup and discounted at the company's 12% cost of capital, is $167,410.71.

Step-by-step explanation:

In assessing if it is proper to use a 40% discount rate for the payment due from the Central Antarctic Republic, one must consider the risk of non-payment due to potential political instability, like a coup d'état. If the controller believes the 40% rate accurately reflects the risk of the coup and the subsequent non-payment likelihood, then this high rate could be justified. However, typically, one would adjust the expected payment based on the probability of the event, rather than adjusting the discount rate drastically.

To calculate the present value of the expected payment considering a 25% chance of a coup, you would first calculate the expected value of the payment, which is the sum of the product of each outcome's value and its probability. Therefore, the expected value of the payment is (0.75 * $250,000) + (0.25 * $0) = $187,500. To discount this at the company's cost of capital (12%), the calculation is $187,500 / (1 + 0.12) = $167,410.71. Thus, the present value of the payment, considering the odds of a coup, would be $167,410.71.