Answer to Question #140282 in Finance for sisi

Question #140282

Investment A offers to pay you $10,000 per year for 8 years, whereas Investment B offers to pay you $12,500 per year for 5 years.

(a) Determine if Investment A or Investment B has the higher present value if the interest rate is 5%.

(b) Determine if Investment A or Investment B has the higher present value if the interest rate is 15%. Show all your calculations.


1
Expert's answer
2020-10-27T08:13:09-0400

Assuming the payments from both investments, A and B, are made at the end of each year, they represent ordinary annuities. The present values required are therefore present values of the given ordinary annuities. The formula for the present value of an ordinary annuity is given as follows:


,


where is the annual payment, is the annual interest rate and is the number of years.


For investments A and B, the following calculations hold.



Project A, whose present value is , has a higher present value than project B, whose present value is


For project A:

PMT = $10,000

i = 5%

n = 8 years






For project B:

PMT = $12,500

i = 5%

n = 5 years







Project A, whose present value is has a higher present value than project B, whose present value is


For project A:

PMT = $10,000

i = 15%

n = 8 years






For project B:

PMT = $12,500

i = 15%

n = 5 years




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