Question

$177,000 $238,000 $311,000 Initial investment (CF) Year (t) $82,000 68,000 55,000 58,000 60,000 Cash inflows (CF) $53,000 70,000 72,000 88,000 94,000 $94,000 94,000 94,000 94,000 94,000 Risk Class Risk Classes and RADRS Description Risk adjusted discount rate (RADR) Lowest risk 10.4% Below-average risk 13.5 Average risk 15.4 Above-average risk 19.2 Highest risk 22.3

Answer 1

NPV is calculated by summing up all the cashflow from the project by discounting each cashflow by appropriate discount rate. in our case the discount rate is RADR.

NPV = - initial investment + CF1/(1+r) +CF2/(1+r)² + CF3/(1+r)³ +CF4/(1+r)⁴ +CF5/(1+r)⁵

RADR for project X = 22.3%

RADR for project Y = 13.5%

RADR for project Z = 15.4%

Risk Adjusted NPV for project X = - 177000 + 82000/(1+22.3%) +68000/(1+22.3%)² + 55000/(1+22.3%)³ +58000/(1+22.3%)⁴ + 60000/(1+22.3%)⁵ = $13,431.76

Risk Adjusted NPV for project Y = - 238000+ 53000/(1+13.5%) +70000/(1+13.5%)² + 72000/(1+13.5%)³ +88000/(1+13.5%)⁴ + 94000/(1+13.5%)⁵ = $15,210.20

Risk Adjusted NPV for project Z = - 177000 + 94000/(1+15.4%) +94000/(1+15.4%)² + 94000/(1+15.4%)³ +94000/(1+15.4%)⁴ + 94000/(1+15.4%)⁵ = $1,141.23

Since the risk adjusted NPV for Y is the highest, firm must take project Y.