Question

a.What is the present value of a $300 perpetuity discounted back to the present at 8 percent?

b.)What is the present value of a perpetual stream of cash flows that pays $4,500 at the end of year one and the annual cash flows grow at a rate of 3% per year​ indefinitely, if the appropriate discount rate is 10%? What if the appropriate discount rate is 8%?

c.How long will it take to pay off a loan of $47,000 at an annual rate of 9% compounded monthly if you make monthly payments of $750?

Answer 1

a) Calculation of PV of perpetuity

PV of perpetuity = Dividend or Coupon per period / Discount rate

= 300/.08

= 3750

b) Calculation of PV of growing perpetuity

PV of growing perpetuity = Dividend or Coupon in year 1 / (Discount rate-growth rate)

= 4500/(.10-.03)

= 4500/.07

= 64285.71

PV of growing perpetuity = Dividend or Coupon in year 1 / (Discount rate-growth rate)

= 4500/(.08-.03)

= 4500/.05

= 90000

c) Calculation of n

EMI = [P * I * (1+I)^N]/[(1+I)^N-1]

P =loan amount or Principal = 47000

I = Interest rate per month = 9/12 = .75%
[To calculate rate per month: if the interest rate per annum is 14%, the per month rate would be 14/(12 x 100)]

N = the number of installments=?

750 = [47000 * .0075 * (1.0075)^N]/[(1.0075)^N-1]

= 352.5 * (1.0075)^N]/[(1.0075)^N-1]

750*1.0075^N-750 = 352.5 * (1.0075)^N

750/1.0075^N = 750-352.2 = 397.5

1.0075^N = 750/39.5 =1.8868

N = log1.8868/log1.0075

= 0.27572586757/0.00324505481

= 84.97 months

= 7.08 years