In: Finance
Year | Project A | Project B |
1 | -400 | -650 |
2 | -528 | 210 |
3 | -219 | 210 |
4 | -150 | 210 |
5 | 1100 | 210 |
6 | 820 | 210 |
7 | 990 | 210 |
8 | -325 | 210 |
WACC 10%
What is NPV,IRR, for both projects and also solve for the crossover rate.
Year | Project A | Present Value for cashflows for Project A=FV/(1+R)^N, here R=10% | Present Value for cashflows for Project A=FV/(1+R)^N, here r=10% | Project B | Present Value for cashflows for Project B=FV/(1+R)^N | Present Value for cashflows for Project B==FV/(1+R)^N |
1 | -400 | -400/(1.1) | -363.6363636 | -650 | -650/1.1 | -590.9090909 |
2 | -528 | -528/(1.1^2) | -436.3636364 | 210 | 210/1.1^2 | 173.553719 |
3 | -219 | -219/(1.1^3) | -164.5379414 | 210 | 210/1.1^3 | 157.7761082 |
4 | -150 | -150/(1.1^4) | -102.4520183 | 210 | 210/1.1^4 | 143.4328256 |
5 | 1100 | 1100/1.1^5 | 683.0134554 | 210 | 210/1.1^5 | 130.3934778 |
6 | 820 | 820/(1.1)^6 | 462.8686226 | 210 | 210/1.1^6 | 118.5395253 |
7 | 990 | 990/(1.1^7) | 508.026537 | 210 | 210/1.1^7 | 107.7632048 |
8 | -325 | -325/(1.1^8) | -151.6148986 | 210 | 210/1.1^8 | 97.96654984 |
NPV= Sum of the present value of all expected incremental cash flows if a project is undertaken | 435.3037568 | 338.5163197 | ||||
IRR= that rate at which NPV=zero i.e Present value of cash inflow =present value of cash outflow( using the BAII plus calculator) | 20.65% | 25.84% | ||||
Or for calculation of IRR you can use trial and error method by putting the present value of cash inflows and outflows sum=0 | 0=-400/(1+r)-528/(1+r)^2-219/(1+r)^3-150/(1+r)^4+1100/(1+r)^5+820/(1+r)^6+990/(1+r)^7-325/(1+r)^8------- Equation 1 | 0=-650/(1+r)+210/(1+r)^2+210/(1+r)^3+210/(1+r)^4+210/(1+r)^5+210/(1+r)^6+210/(1+r)^7+210/(1+r)^8----- equation 2 | ||||
Solving for r using trial and error method | Solving for r using trial and error method | |||||
Since NPV is positive so in order to make it equal to zero assume r =20% and the calculate NPV using equation 1 | Since NPV is positive so in order to make it equal to zero assume r =25% and the calculate NPV using equation 1 | |||||
Here solving at r=20%, NPV=18.3138 | Here solving at r=25%, NPV=11.0713 | |||||
Since NPV is still positive i.e 18.3138 increase the rate by 1 per suppose 21% | Since NPV is still positive i.e 11.07138 increase the rate by 1 per suppose 26% | |||||
Now again calculate NPV at 21% rate | Now again calculate NPV at 26% rate | |||||
Here solving at r=21%, NPV=-9.46215 | Here solving at r=26%, NPV=-1.9871 | |||||
Now NPV is negative, use linear interpolation | Now NPV is negative, use linear interpolation | |||||
FORMULA LINEAR INTERPOLATION: Lower rate+(Required Actual NPV-lower rate NPV)*{(Higher rate- lower rate)}/(Higher rate NPV- Lower rate NPV) | FORMULA LINEAR INTERPOLATION:Lower rate+(Required Actual NPV-lower rate NPV)*{(Higher rate- lower rate)}/(Higher rate NPV- Lower rate NPV) | |||||
20.7% | 25.8% |
Crossover rate: Discount rate where NPV of Project A= NPV of Project B. | |||
To calculate crossover rate , subtract cash flows of Project B from those of Project A and calculate IRR of the difference | |||
Project A- Project B | |||
Year | Project A | Project B | Difference |
1 | -400 | -650 | 250 |
2 | -528 | 210 | -738 |
3 | -219 | 210 | -429 |
4 | -150 | 210 | -360 |
5 | 1100 | 210 | 890 |
6 | 820 | 210 | 610 |
7 | 990 | 210 | 780 |
8 | -325 | 210 | -535 |
For crossover rate compute IRR using using the BAII plus calculator | 14.75% | ||
Or for calculation of IRR you can use trial and error method as mentioned in part 2 for IRR calculation | 0=250/(1+r)-738/(1+r)^2-429/(1+r)^3-360/(1+r)^4+890/(1+r)^5+610/(1+r)^6 +780/(1+r)^7-535/(1+r)^8------- Equation 3 |