Question

A firm must choose between two investment alternatives, each costing $90,000. The first alternative generates $25,000 a year for five years. The second pays one large lump sum of $142,800 at the end of the fifth year. If the firm can raise the required funds to make the investment at an annual cost of 9 percent, what are the present values of two investment alternatives? Use Appendix B and Appendix D to answer the question. Round your answers to the nearest dollar.
PV_{(First alternative)}: $  
PV_{(Second alternative)}: $  

Which alternative should be preferred?
The (first or second) alternative should be preferred.

Answer 1

Answer : Calculation of Present Value of First Alternative that pays $25000 a year for 5 years :

Present Value of annuity = Periodic payment * { [1 - (1+r)^-n ] / r }

Where,

Periodic payment = 25000

r is the rate of interest i.e 9% or 0.09

n is the number of payments i.e 5

Present value of annuity = 25000 * { [1- (1+0.09)^-5 ] / 0.09 }

= 25000 * {[1 - 0.649931] / 0.09}

= 25000 * {0.350069 / 0.09}

= 25000 * 3.889651

Present value of annuity = 97241.28 or 97241

Calculation of Present value of second Alternative

Present Value = Future Value / (1 + rate)^number of years

= 142800 / (1 + 0.09)^5

= 142800 / 1.538624

= 92810.20 or 92810

First Alternative should be choosen as it has higher Present Value .