Dr. Joe Schmo is a finance professor at a small Southern liberal arts university. A student...

Dr. Joe Schmo is a finance professor at a small Southern liberal arts university. A student who has performed poorly in the introductory finance class has offered to pay Dr. Schmo for a better grade. Dr. Schmo presented the student with this agreement to sell a better grade: Since he would be fired from his position, he would lose his salary and benefits. His salary is $74,000 per year, paid in equal payments at the end of the each month. His salary is expected to keep pace with inflation. You may assume the monthly salary payments increase at the inflation rate. His benefits amount to $23,000 per year, and the benefit payments occur at the beginning of each year. The benefits will also increase at the rate of inflation. He expects to work for another 15 years. Assume the required return is 5.4 percent and the inflation rate is 3.1 percent. All rates are effective annual rates. Dr. Schmo will sell the student a better grade if the student pays the present value of the future lost salary and benefits. How much will the student have to pay for a better grade

Solutions

Expert Solution

Present Value of Monthly Salary today = First month Salary * (1 / (Monthly required Rate - Monthly Inflation)) * [ 1 - ((1+ Monthly Inflation)/(1 + Monthly Required return))^Periods)

Present Value of Monthly Salary today = 74000/12 * (1 / (0.0045 - 0.002583)) * [ 1 - ((1+0.002583)/(1 + 0.0045))^180)

Present Value of Monthly Salary today = 3217391.30 * [1 - (0.998092)^180)

Present Value of Monthly Salary today = 3217391.30 * [1 - 0.709083]

Present Value of Monthly Salary today = $935993.48

Present Value of Annual Benefits today = Current benefits * (1 + Inflation) (1 / (required Rate - Inflation)) * [ 1 - ((1+ Inflation)/(1 + Required return))^years) + [Current Benefits)

Present Value of Annual Benefits today = 23000 * (1 + 0.031) (1 / (0.054 - 0.031)) * [ 1 - ((1+ 0.031)/(1 + 0.054))^14) + 23000

Present Value of Annual Benefits today = $1031000 * [ 1 - (0.9782)^14) + 23000

Present Value of Annual Benefits today = $1031000 * [ 1 - 0.7343) + 23000

Present Value of Annual Benefits today = $273972.90 + 23000

Present Value of Annual Benefits today = $296972.90

How much will the student have to pay for a better grade = $935993.48 + 296972.90

How much will the student have to pay for a better grade = $1232966.38

Please comment if you face any difficulty and please dont forget to upvote

jeff jeffy answered 1 year ago

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