Solutions to mini case 1 AFM (grade: 10/10)

Advanced Financial Management - Mini-case week 1 Isabella Arnold, 2665767


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Question 1:
1. What are the NPV, PI, and IRR for projects A and B? What has caused the ranking
conflicts? Should project A or B be chosen? Assume that these projects are
not considered under a capital constraint.
𝐶𝐹! 𝐶𝐹"
𝑁𝑃𝑉 = −𝐼 + + ⋯ +
(1 + 𝑟)! (1 + 𝑟)"
$%&'' $%&'' ,''''
e.g. 𝑁𝑃𝑉# = −75000 + (!)!'%) + (!)!'%)! + (!)!'%)" = 42081,14

I did the same for project B, taking the investment and CFs of project B into account.
The NPV for project A: 42.081,14
The NPV for project B: 36.908,34


𝑁𝑃𝑉 + 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
𝑃𝐼 =
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
-$'%!,!-)/&'''
e.g. 𝑃𝐼# = /&'''
= 1.56

I did the same for project B, taking the NPV and investment of project B into account.
The PI for project A: 1.56
The PI for project B: 1.49


𝐶𝐹! 𝐶𝐹"
𝑁𝑃𝑉 = −𝐼 + + ⋯+ =0
(1 + 𝐼𝑅𝑅)! (1 + 𝐼𝑅𝑅)"
Solve for IRR
$%&'' $%&'' $%&''
e.g. 𝑁𝑃𝑉# = −75000 + (!)011) + (!)011)! + (!)011)" = 0 → 𝑆𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝐼𝑅𝑅 = 33.63%

I did the same for project B, taking the investment and CFs of project B into account.
The IRR for project A: 33.63%
The IRR for project B: 36.31%

, Advanced Financial Management - Mini-case week 1 Isabella Arnold, 2665767


- The fact that in project A the last cash flow is a rather high one explains the difference
in the internal rates of return as we can see that in project B the cash flows remain the
same at each t. The higher a cash flow is in time, the lower the PV of that cash flow
will be, which explains the lower IRR in project A.
- Project A should be chosen as we are seeking for wealth creation, and project A
creates more wealth. The PI for project A is also higher which implies a good project.


Question 2:
2. What are the NPV, PI, and IRR for projects C and D? Should project C or
D be chosen? Assume that these projects are not considered under a capital
constraint.
𝐶𝐹! 𝐶𝐹"
𝑁𝑃𝑉 = −𝐼 + + ⋯+
(1 + 𝑟)! (1 + 𝑟)"
$&'''
e.g. 𝑁𝑃𝑉2 = −20000 + (!)!'%) = 2727,27

I did the same for project D, taking the investment and CFs of project D into account.
The NPV for project C: 2727,27
The NPV for project D: 1090,91


𝑁𝑃𝑉 + 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
𝑃𝐼 =
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
$/$/,$/)$''''
e.g. 𝑃𝐼2 = $''''
= 1.14

I did the same for project D, taking the NPV and investment of project D into account.
The PI for project C: 1.14
The PI for project D: 1.14


𝐶𝐹! 𝐶𝐹"
𝑁𝑃𝑉 = −𝐼 + + ⋯+ =0
(1 + 𝐼𝑅𝑅)! (1 + 𝐼𝑅𝑅)"
Solve for IRR
$&'''
e.g. 𝑁𝑃𝑉2 = −20000 + (!)011) = 0 → 𝑆𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝐼𝑅𝑅 = 25%

I did the same for project D, taking the investment and CFs of project D into account.
The IRR for project C: 25%
The IRR for project D: 25%