Question

Problem 17 Intro WH Smith Company is evaluating three projects: A, B, C, with cash flows as in the table. Each project requires an initial investment of $99,000 and has a required return of 9%. given C Year A B 0 20,000 50,000 1 40,000 50,000 40,000 2 20,000 50,000 40,000 3 10,000 40,000 40,000 4

Answer 1

NPV of a project is the sum of present values of all cash flows. NPV of any project can be calculated using the below formula:

$NPV = C_{0} + \frac{C_{1}}{(1+r)}+ \frac{C_{2}}{(1+r)^{2}}+ \frac{C_{3}}{(1+r)^{3}}+ \frac{C_{4}}{(1+r)^{4}}$

For all the projects A, B, C, and D C₀ = -99,000

For A

C₀ = -99000, C₁ = 50000, C₂ = 40000, C₃ = 20000, C₄ = 10000

$NPV_{A} = -99000 + \frac{50000}{(1+0.09)}+ \frac{40000}{(1+0.09)^{2}}+ \frac{20000}{(1+0.09)^{3}}+ \frac{10000}{(1+0.09)^{4}}$

NPV_A = -99000+45871.5596330275+33667.1997306623+15443.6696012213+7084.25211065196 = 3066.68107556

For B

C₀ = -99000, C₁ = 0, C₂ = 50000, C₃ = 50000, C₄ = 40000

$NPV_{A} = -99000 + \frac{0}{(1+0.09)}+ \frac{50000}{(1+0.09)^{2}}+ \frac{50000}{(1+0.09)^{3}}+ \frac{40000}{(1+0.09)^{4}}$

NPV_B = -99000+0+42083.999663328+38609.1740030532+28337.0084426079 = 10030.1821089891

For C

C₀ = -99000, C₁ = 20000, C₂ = 40000, C₃ = 40000, C₄ = 40000

$NPV_{C} = -99000 + \frac{20000}{(1+0.09)}+ \frac{40000}{(1+0.09)^{2}}+ \frac{40000}{(1+0.09)^{3}}+ \frac{40000}{(1+0.09)^{4}}$

NPV_C = -99000+18348.623853211+33667.1997306623+30887.3392024426+28337.0084426079 = 12240.1712289238

Part 5 - NPV_A = 3067

Part 6 - NPV_B = 10030

Part 7 - NPV_C = 12240

Part 8 - Project C is best based on the NPV rule as it has the highest NPV