Question

A project has annual cash flows of $7,000 for the next 10 years and then $8,500 each year for the following 10 years. The IRR of this 20-year project is 13.37%. If the firm's WACC is 10%, what is the project's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations. $

Answer 1

Internal rate of return or IRR is the percentage rate at which the net present value (NPV) equals to zero.
NPV=-Initial cash outflow+Present value of future cash flows
=>0=-Initial cash outflow+Present value of future cash flows
=>Initial cash outflow=Present value of future cash flows
Present value of future cash flows is calculated by taking summation of (Cash flow in year n)/(1+IRR)^(Year n)

=$7,000/(1+13.37%)^1+$7,000/(1+13.37%)^2+$7,000/(1+13.37%)^3+$7,000/(1+13.37%)^4+$7,000/(1+13.37%)^5+$7,000/(1+13.37%)^6+$7,000/(1+13.37%)^7+$7,000/(1+13.37%)^8+$7,000/(1+13.37%)^9+$7,000/(1+13.37%)^10+$8,500/(1+13.37%)^11+$8,500/(1+13.37%)^12+$8,500/(1+13.37%)^13+$8,500/(1+13.37%)^14+$8,500/(1+13.37%)^15+$8,500/(1+13.37%)^16+$8,500/(1+13.37%)^17+$8,500/(1+13.37%)^18+$8,500/(1+13.37%)^19+$8,500/(1+13.37%)^20

=$7,000/(1.1337)^1+$7,000/(1.1337)^2+$7,000/(1.1337)^3+$7,000/(1.1337)^4+$7,000/(1.1337)^5+$7,000/(1.1337)^6+$7,000/(1.1337)^7+$7,000/(1.1337)^8+$7,000/(1.1337)^9+$7,000/(1.1337)^10+$8,500/(1.1337)^11+$8,500/(1.1337)^12+$8,500/(1.1337)^13+$8,500/(1.1337)^14+$8,500/(1.1337)^15+$8,500/(1.1337)^16+$8,500/(1.1337)^17+$8,500/(1.1337)^18+$8,500/(1.1337)^19+$8,500/(1.1337)^20

=$7,000/1.1337+$7,000/1.28527569+$7,000/1.45711705+$7,000/1.651933599+$7,000/1.872797122+$7,000/2.123190097+$7,000/2.407060613+$7,000/2.728884617+$7,000/3.09373649+$7,000/3.507369058+$8,500/3.976304302+$8,500/4.507936187+$8,500/5.110647255+$8,500/5.793940793+$8,500/6.568590677+$8,500/7.44681125+$8,500/8.442449914+$8,500/9.571205468+$8,500/10.85087564+$8,500/12.30163771

=$6174.472965+$5446.302342+$4804.006651+$4237.458457+$3737.724667+$3296.925702+$2908.11123+$2565.150595+$2262.636143+$1995.797957+$2137.663356+$1885.563515+$1663.194421+$1467.049855+$1294.037095+$1141.428152+$1006.816752+$888.080402+$783.3469189+$690.9649106
=$50386.73208

NPV=-Initial cash outflow+Present value of future cash flows
Using IRR we get the initial cash outflow as $50386.73208
Now we will use weighted average cost of capital WACC as the discount rate to calculate the NPV.
NPV=-Initial cash outflow +Summation of (Cash flow in year n)/(1+WACC)^(Year n)

Given that WACC=10%
NPV=-$50386.73208+$7,000/(1+10%)^1+$7,000/(1+10%)^2+$7,000/(1+10%)^3+$7,000/(1+10%)^4+$7,000/(1+10%)^5+$7,000/(1+10%)^6+$7,000/(1+10%)^7+$7,000/(1+10%)^8+$7,000/(1+10%)^9+$7,000/(1+10%)^10+$8,500/(1+10%)^11+$8,500/(1+10%)^12+$8,500/(1+10%)^13+$8,500/(1+10%)^14+$8,500/(1+10%)^15+$8,500/(1+10%)^16+$8,500/(1+10%)^17+$8,500/(1+10%)^18+$8,500/(1+10%)^19+$8,500/(1+10%)^20

=-$50386.73208+$7,000/(1.1)^1+$7,000/(1.1)^2+$7,000/(1.1)^3+$7,000/(1.1)^4+$7,000/(1.1)^5+$7,000/(1.1)^6+$7,000/(1.1)^7+$7,000/(1.1)^8+$7,000/(1.1)^9+$7,000/(1.1)^10+$8,500/(1.1)^11+$8,500/(1.1)^12+$8,500/(1.1)^13+$8,500/(1.1)^14+$8,500/(1.1)^15+$8,500/(1.1)^16+$8,500/(1.1)^17+$8,500/(1.1)^18+$8,500/(1.1)^19+$8,500/(1.1)^20

=-$50386.73208+$7,000/1.1+$7,000/1.21+$7,000/1.331+$7,000/1.4641+$7,000/1.61051+$7,000/1.771561+$7,000/1.9487171+$7,000/2.14358881+$7,000/2.357947691+$7,000/2.59374246+$8,500/2.853116706+$8,500/3.138428377+$8,500/3.452271214+$8,500/3.797498336+$8,500/4.177248169+$8,500/4.594972986+$8,500/5.054470285+$8,500/5.559917313+$8,500/6.115909045+$8,500/6.727499949

=-$50386.73208+$6363.636364+$5785.123967+$5259.203606+$4781.094188+$4346.449261+$3951.31751+$3592.106828+$3265.551661+$2968.683329+$2698.803026+$2979.198146+$2708.36195+$2462.147228+$2238.315662+$2034.83242+$1849.847654+$1681.679686+$1528.799714+$1389.817922+$1263.470838
=>NPV=$12761.70888 or $12762 (Rounded to nearest cent)