MPV_APPE 2017
Discounting – problems for practice
1. We can choose between 1000 € today and 3000 € in 30 years. We consider r = 4%. Which
option has higher value and by how much?
(Solution: 1000 € vs. 924.96 €, first option by 75.04 €)
2. Which is more: 1000 € in t = 6 with r = 5% or 1500 € in t = 4 with r = 20%? By how much?
(Solution: 746.22 € vs. 723.38 €, first option by 22.84 €)
3. What is the value of 1000 € in 20 years with r = (1, 2, 3, 4, 5, 10, 20, 30, 50)%?
(Solution: 819.54; 672.97; 553.68; 456.39; 376.89; 148.64; 26.08; 5.26; 0.30 €)
Payback period – problems for practice
1. We have project with costs 1000, net annual income of 220 and lifetime 7 years. What is
simple and real payback period with r = 9% is the project acceptable?
(Solution: PBs = 5 years, PBr = 7 years, project is acceptable in both cases)
2. We have project with costs 400 and decreasing net incomes of 100, 90, 80,..., 10. What is the
simple and real PB with r = 8% and is the project acceptable with lifetime of 10 years?
(Solution: PBs = 5 years, PBr = 9 years, project is acceptable in both cases)
3. We have project with costs 300 and increasing net income 10, 20, 30, 40,.... What is simple
and real payback period with r = 7%?
(Solution: PBs = 8 years, PBr = 10 years)
NPV – problems for practice
1. Calculate NPV of project with investment costs of 500 and net income annual 200 for 5 year
period with discount rate of 14%.
(Solution: NPV = 186.62)
2. Choose preferable project according to the NPV criterion, all have initial investment of 200
and then: A) lifetime 2 years and CF (+150; +200); B) lifetime 3 years and CF (+100; +100;
+250); C) lifetime 6 years and CF (+300; -200; +300; +100; +100; +100). Discount rate is 7%.
*hint: first adjust the project to the same lifetime and then calculate NPVs.
(Solution: C = 364.8; B = 335.8; A = 302.8)
3. Compare projects based on NPV: A) lifetime 3 years and cash flow (-300; 0; +250; +500); B)
lifetime 4 years and cash flow (-300; -200; +1000; 0; +100); C) lifetime 6 years and investment
costs 300 and annual cash flow +210. Use discount rate 2%. Which project is the best?
(Solution: C = 1654; B = 1548; A = 1509)
MPV_APPE 2017
Rentability index – problems for practice
1. We have 2 projects: A) costs 50, incomes +100; +200; B) costs 500; incomes +900; +900.
Discount rate is 1%. Which project would you choose based on Ri? And which based on NPV?
(Solution: Ri: A = 4.901; B = 2.547; NPV: B = 1273; A = 245)
2. Municipality can choose between 3 projects, sort them according to the Ri with r = 19%:
Period 0 1 2 3 4 5
Project A -20 +16 +11 +6
Project B -30 +11 +22 +11 0 +6
Project C -40 +10 +10 +10 +30
(Solution: A = 0.239; B = 0.127; C = -0.091)
3. Choose the best project according to the Rentability index: A) lifetime 2 years and CF (-200;
+150; +80); B) lifetime 3 years and CF (-400; +100; +100; +300); C) with lifetime 6 years and
CF (-500; +300; -200; +300; +100; +100; +100). Discount rate is 0.07.
(Solution: C = 0.130; B = 0.064; A = 0.050)
IRR – problems for practice
1. Sort the projects based on their IRR:
Period 0 1 2 3 4 5
Project A -20 +10 +10 +10
Project B -30 +10 +20 +5 +5 +15
Project C -40 +10 +30 +20 +15
Project D -50 +10 +40 +10 +10 +10
(Solution: C = 29.72%; B = 25.55%; A = 23.38%; D = 20.74%)
2. We have project with costs 1000, net annual income 220 and lifetime 5 years. Calculate IRR
of this project. Does the project pay off if the general discount rate is 5%?
(Solution: project does not pay off, IRR is 3.26%)
3. We have project with cash flow in individual years: -1500; +5400; -6465; +2574. Find all IRRs
of this project.
(Solution: 10%; 20%; 30%)