Question

The following table provides the projected numbers of widget machines sold per year for next 6 years. Suppose the widget price today is $15, the annual inflation rate and the nominal discount rate will be 4% and 12% respectively for next 6 years.

Year Widgets sold

0

1 100

2 125

3 150

4 160

5 170

6 200

(a)Calculate the anticipated nominal cash flows and anticipated real cash flows in year 0 dollars for next 6 years.

(b) Use the nominal cash flows you get to calculate NPV and IRR.

(c) Use the real cash flows you get to calculate NPV and IRR.

(d) What is the relationship between NPVs you get from (b) and (c)? What is the relationship between IRRs you get from (b) and (c)?

Answer 1

Real rate=(1+nominal)/(1+inflation)-1=1.12/1.04-1=7.6923077%
Here, the initial investment is not given. Assuming it to be zero
Nominal Cash flows:
Year 0:-Initial Investment=0
Year 1:15*1.04*100=1560
Year 2:15*1.04^2*125=2028
Year 3:15*1.04^3*150=2530.944
Year 4:15*1.04^4*160=2807.660544
Year 5:15*1.04^5*170=3102.464901
Year 6:15*1.04^6*200=3795.957055

NPV=-Initial Investment+1560/1.12+2028/1.12^2+2530.944/1.12^3+2807.660544/1.12^4+3102.464901/1.12^5+3795.957055/1.12^6=10278.93319
IRR:
0=-Initial Investment+1560/(1+IRR)+2028/(1+IRR)^2+2530.944/(1+IRR)^3+2807.660544/(1+IRR)^4+3102.464901/(1+IRR)^5+3795.957055/(1+IRR)^6
If initial investment is zero, IRR cannot be found out

Real Cash Flows:
Year 0:0
Year 1:15*100=1500
Year 2:15*125=1875
Year 3:15*150=2250
Year 4:15*160=2400
Year 5:15*170=2550
Year 6:15*200=3000

NPV=-Initial Investment+1500/(1+7.6923077%)+1875/(1+7.6923077%)^2+2250/(1+7.6923077%)^3+2400/(1+7.6923077%)^4+2550/(1+7.6923077%)^5+3000/(1+7.6923077%)^6=10278.93319
IRR:
0=-Initial Investment+1500/(1+IRR)+1875/(1+IRR)^2+2250/(1+IRR)^3+2400/(1+IRR)^4+2550/(1+IRR)^5+3000/(1+IRR)^6
If initial investment is zero, IRR cannot be found out

NPVs found in both the parts are same
IRR found in part b) is nominal rate and IRR found in part c) is real rate..IRR in c)=IRR in b)/(1+inflation)