Answer to Question #263280 in Financial Math for Kwabenya

Question

A company wants to undertake an investment and has two projects under consideration. Project 1 will have a useful life of 7 years whereas project 2 would have a useful life of 6 years. Project 1 would also require an initial investment of GHc300,000 plus an additional repair cost of GHc20,000 on year 6. Project 2 would also require an initial investment of GHc240,000 plus an additional repair cost of GHc25,000 in years 4 and 5. Project 1 and 2 have an estimated salvage value of GHc5000 and GHC3000 respectively. Due to different project risk, project 1 and project 2 would be evaluated at an interest rate of 10% and 12% per year respectively. Project profits are estimated to be GHc100,000 and GHc100,000 per year respectively for both projects starting at the end of year 1 till the end of their respective project lifespans.

Using the NPV approach, determine which project the company must invest in.

Answer 1

NVP refers to the net present value.

present value=future value/[(1+ interest rate)ⁿ ]

project 1

useful life-7 years

initial investment-GHC 300000

repair cost-GHC 20000 on year 6

salvage value -GHC 5000

interest value-10% per year

projected profits-GHC100000 at the end of each year from year one to year six.

TOTAL PV=100000/1.1¹+100000/1.1²+100000/1.1³+100000/1.12³+100000/1.1⁴+100000/1.1⁵+100000/1.1⁶+100000/1.1⁷

TOTAL PV=90909.09+82644.63+75131.48+68301.35+62092.52+56447.39

TOTAL PV =435526.46

NET PRESENT VALUE=CASH INFLOW -CASH OUTFLOW

NET PRESENT VALUE=TOTAL VP-(INITIAL INVESTMENT+REPAIRS+SALVAGE PRICE)

NVP=435526.46-(300000+20000+5000)

NVP=435526.46-325000

NVP=110526.46

PROJECT 2

useful life-6 years

initial investment-GHC 240000

repairs-GHC25000 in year 4 and 5

salvage value-GHC 3000

interest rate-12%

projected profits-GHC 100000 at the end of each year from year one

TOTALPV=100000/1.12¹⁺100000/1.12²+100000/1.12³+100000/1.12⁴+100000/1.12⁵+100000/1.12⁶+100000/1.12⁷

total PV= 89285.71 + 79719.38 + 71178.02 +63552.59 + 56742.69 +50663.11+45234.92

total PV=456383.42

NVP=CASH INFLOW-CASH OUTFLOW

NVP= TOTAL VP-(INITIAL INVESTMENT+REPAIRS+SALVAGE PRICE)

NVP=456383.42-(240000+25000+25000+3000)

NVP=456383.42-293000

NVP=GHC 163383.42

Considering the the net present value of project 1 and 2 the company should invest in project 2 because it has a higher return compared to project 1.