Question

Question 13

Your business will pay you distributions of $19,000 in 6 months and another $5,000 in 19 months. If the discount rate is 8% per annum (compounding monthly) for the first 9 months, and 11% per annum (compounding monthly) for the next 10 months, what single amount received today would be equal to the two proposed payments? (answer to nearest whole dollar; do not use $ sign or commas)

Answer 1

discount rate given = 8%

since it is monthly compounding discount rate = 8 / 12 = 0.66667% (for the first 9 months)

we should calculate present value using above discount rate

present value = 1 / (1+r)^n

Where r = interest rate , n = time period

so present value of first cash flow = 19000 / (1.0066667)^9 = 17897.08

discount rate for the next 10 months = 11% per annum so per month = 11 / 12 = 0.91667%

we use discount rates as 0.66667% for first nine months and then 0.91667% for next 10 months

so present value of second cash flow = 5000 / [(1.0066667)^9 x (1.0091667)^10 ] = 4299.02

total present value = 17897.08 + 4299.02 = 22196.1 or 22196(rounded to nearest dollar)