(A)
The payback is 35,000/5,000= 7 years
Computation of the NPV :
NPV= -35,000 + Σ 5,000 / ( 1 + 12%)^ 15 i=1 NPV = $- 945. 67
Computation of the IRR :
0= -35,000 + Σ 5,000 / ( 1 + IRR)^ 15 i=12 IRR= 11.49%
The NPV of this project is negative and the IRR is lower then the Cost of Capital (12%) Rainbow products shouldn’t go for it.
(B)
Based on the perpetuity formula we can compute the PV in this case :
Computation of the PV :
PV= Cash flow per year/ cost of capital)
=4,500 / 0.12
= $37,500
Computation of the NPV :
NPV= -Initial investment + PV
= -35,000 + 37,500
NPV=$2,500
Rainbow products could buy this machine with the service contract if they intent to use it in the long-run.
(C)
Computation of the PV :
PV= C/ k-g
In this case C (end of year perpetuity payout) = 5,000-1,000= $4,000 k= 12%, discount rate g= 4%, growing rate at perpetuity
PV= 4,000 / (0.12-0.04) = $50,000
Computation of the NPV :
NPV= -35,000+ 50,000 = $15,000
The rainbow products company should invest in this project because its NPV is largely positive because of the reinvestment of 20% of the annual cost, even though this is in a very long term vision.
2.
•Computation of the IRRs (with financial calculator) :
Project,
-Add a New Window : IRR = 34.61%
-Update Existing Equipment : IRR = 18.01%
-Build a new stand : IRR = 31.20%
-Rent a larger stand: IRR = 1207%
All projects are acceptable because all the IRRs are higher than the discount rate(15%) Looking at the internal rate o return of each project, rent a larger stand Is the project with the highest IRR.
•Computation of the NPVs (with financial calculator) :
Project,
-Add a New Window : NPV = $ 25,461.9
-Update Existing Equipment : NPV = $ 2,514.18
-Build a new stand : NPV = $ 34,825.75
-Rent a larger stand: NPV = $ 28,469.87
All the projects are acceptable because all the NPVs are positive Looking at the net present value of each project, build a new stand Is the project with the highest NPV •The difference