Question

a firm must choose between two investment alternatives, each costing $95,000. the first alternative generates $35,000 a year for 4 years. the second pays one large lump sum of $160,800 at the end of the fourth year. if the firm can raise the required funds to make the investment at an annual cost of 9% 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?

Answer 1

firm can raise the required funds to make the investment at an annual cost of 9%

discount rate = r = 9%

First alternative

The cash flows of the First alternative are:

Year	0	1	2	3	4
Cash flow	-95000	35000	35000	35000	35000

Cash flows are: C₀ = -95000, C₁ = 35000, C₂ = 35000, C₃ = 35000, C₄ = 35000

The present value of first alternative = PV = C₀ + C₁/(1+r)¹ + C₂/(1+r)² + C₃/(1+r)³ + C₄/(1+r)⁴

PV (first alternative) = -95000 + 35000/(1.09)¹ + 35000/(1.09)² + 35000/(1.09)³ + 35000/(1.09)⁴ = -95000 + 32110.0917431193 + 29458.7997643296 + 27026.4218021372 + 24794.8823872819 = 18390.195696868

PV(first alternative) = 18390

Second alternative

The cash flows of second alternative are:

Year	0	1	2	3	4
Cash flow	-95000				160800

Cash flows are: C₀ = -95000, C₄ = 160800

The present value of second alternative = PV = C₀ + C₄/(1+r)⁴ = -95000 + 160800/(1.09)⁴ = -95000 + 113914.773939284 = 18914.7739392836

PV(second alternative) = 18915

Since the present value of the second alternative is greater than that of the first alternative. So, the second alternative should be preferred