Please show your work and write solutions in details, including formulas and how
ID: 2651407 • Letter: P
Question
Please show your work and write solutions in details, including formulas and how you plug numbers, given in each question, into these formulas. Please, write short VERBAL conclusion at the end of each problem summarizing your answer in words. Verbal answers are not substitute for the quantitative solution.
Question 2
Having proved yourself to be an exemplary student, Pace offers you a choice between an outright gift of $1,000, or a $7,000 interest free loan to be paid back in seven equal annual installments of $1,000 each.
a) Which alternative do you prefer if your discount rate is 3%?
b) Which alternative do you prefer if your discount rate is 10%?
c) At what discount rate you will be indifferent between the two alternatives?
Explanation / Answer
a. If the discount rate is 3%
Alternative 1: to take a gift of $1000
Alternative 2: To take the loan $7000 and repaid @1000 per month for next 7 month
Calculation of alternative 2
As the above calculation shows that the present value of all the cash flow is $769.71 which is less than $ 1000 so i have to take alternative 1 i.e. to take the gift of $ 1000 rather than take a loan of $ 7000.
Point (b)
As the above calculation shows that the present value of all the cash flow is $2131 which is more than $ 1000 so i have to take alternative 2 i.e. to take the loan of $7000
Point no (c ).
In order to determine the discount rate where the both the alternative would be indifferent. In order to calculate the same we have to calculate NEt present value of the project.
Please find below the calculation where @4% the sum of the present value of the cash flows would be same as the alternative 1 hence @4% discount rate both the alternative would be indifferent.
Discount rate@3% 3% Period cash flow Present value (Cashflow/(1+disc rate)^n) 0 $7,000 7000 1 ($1,000) -970.874 2 ($1,000) -942.596 3 ($1,000) -915.142 4 ($1,000) -888.487 5 ($1,000) -862.609 6 ($1,000) -837.484 7 ($1,000) -813.092 Profit 769.717