Question

In: Finance

Year Project A Project B 1 -400 -650 2 -528 210 3 -219 210 4 -150...

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.

Solutions

Expert Solution

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

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