Question

Risk-adjusted discount rates—Basic Country Wallpapers is considering investing in one of three mutually exclusive projects, E, F, and G. The firm's cost of capital, r, is 14.6%, and the risk-free rate, RF, is 10.4%. The firm has gathered the following basic cash flow and risk index data for each project 2 a. Find the net present value (NPV) of each project using the firm's cost of capital. Which project is preferred in this situation? b. The firm uses the following equation to determine the risk-adjusted discount rate, RADR, for each projectſ: RADR; = Rp+RI;* (r-RF) where Re = risk-free rate of return, R; = risk index for project, and r = cost of capital. c. Use the RADR for each project to determine its risk-adjusted NPV. Which project is preferable in this situation? d. Compare and discuss your findings in parts (a) and (c). Which project do you recommend that the firm accept? X i Data Table (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Project (i) $15,100 Initial investment (CF) Year(t) ني نية $6,400 6,400 6,400 6,400 1.75 $11,000 $19,000 Cash inflows (CF) $6,400 $4,500 4,200 6,500 4.900 7,100 2,400 12,600 1.04 0.56 ا Risk index (R!;) Print Done Press Continue to see more. 14 pemaining Continue

Answer 1

Cost of Capital = 14.60% Cashflows PV factor @ Discounted Cashflows Year E F G 14.60% LE F 0 -$15.100 -$11,000 $19.000 1.0000 -$15.100.00 - $11,000.00 -$19,000.00 $6,400 $6.400 $4,500 0.8726 $5,584.64 $5,584.64 $3,926.70 $6,400 $4,200 $6,500 0.7614 $4.873.16 $3.198.01 $4.949.30 $6,400 $4,900 $7.100 0.6644 $4,252.32 $3,255.68 $4.717.42 4 $6,400 $2,400 $12,600 0.5798 $3,710.58 $1,391.47 $7,305.20 NPV $3,320.70 $2,429.80 $1,898.62 Since Project E gives higher NPV, Project E shall be preferred.

b Cost of Capital (r ) = Risk Free Rate (RA) = 14.60% 10.40% f - Rf= 4.20% RADRj = Rf-RIj (r - Rf) Projects RI Computation RADRİ 1.75 = 0.104 + (1.75 x 0.042)] 17.75% 1.041 = 0.104 - (1.04 x 0.042)| 14.77% 0.56 = 0.104 + (0.56 x 0.042) 12.75%

D) When Cost of Capital is used as the Discount rate, Project E has to be preferred. While, Risk Adjusted Discount rate is used, Project G shall be selected.So in order to find which project to be selected, the following method can be followed (to be on the safer side.)

E Year PV factor @ Discounted PV factor Cash Flows Cash Flows 17.75% Cashflows "S @ 14.77% -$15.100 -$15.100 -$11,000 $6,400 0.8493 $5,436 $6,400 0.8713 $6,400 0.7213 $4.616 $4,200 0.7592 $6,400 0.6126 $3.921 $4,900 0.6615 $6,400 0.5203 $3,330 $2,400 0.5764 $2,202 Since Project G gives higher NPV, Project G shall be preferred. Discounted Cash Flows Cashflows -$11,000 -$19,000 $5,576 $4,500 $3.189 $6,500 $3,241 $7.100 $1,383 $12.600 S2,390 PV factor @ Discounted 12.75% Cashflows -$19.000 0.8869 $3.991 0.7866 $5,113 0.6976 $4,953 0.6187 $7,796 $2,853 NPV

The NPV of the project with discount rate of (higher of Cost of capital or RADRj ) can be compared:

Project Selection for Comparison $2,202.40 Discount rate 14.60% 17.75% 14.60% 12.75% NPV $3.320.70 $2,202.40 $1.898.62 $2,852.53 $1,898.62 Project E can be selected

The Project can be Compared on any other basis also in the opinion of the management. the answer may change because of such opinion.