Question

a step change from 15 to

Problem: For a proposed investment, net profit after tax is assumed to be 2 million dolars and constant for 10 years of service life of the project. Annual depreciation during the 10-year sevice life is $400,000. Annual interest rate is 10%. a Calculate the future value and the present value of annual cash flow if the annual cash flow occurs at the end of each year and the interest is discrete Repeat part a if the interest and the cash flow are continuous

Answer 1

a). Annual cash flow (CF) = after-tax net profit + depreciation = 2,000,000 + 400,000 = 2,400,000

PMT = 2,400,000; N = 10; rate = 10%, solve for PV. PV = 14,746,961.05

PMT = 2,400,000; N = 10; rate = 10%, solve for FV. FV = 38,249,819.04

b). PV with continuous compounding of continuous cash flows

= $\int_{0}^{10}CFe^{-rt}dt$ where CF = 2,400,000 and r = 10%

PV = $2,400,000\int_{0}^{10}e^{-0.10t}dt$ =

= -24,000,000*[0.3679 -1] = 15,170,893.41

Fv with continuous compounding of continuous cash flows

= $\int_{0}^{10}CFe^{rt}dt$ = $2,400,000\int_{0}^{10}e^{0.10t}dt$ =

= 24,000,000*[2.7183 -1] = 41,238,763.88