Question

You are looking at forecasts prepared by your business development unit

You suspect that these numbers are inflated, not deflated. Your estimate of the inflation rate is 2.5%.

Year 1 2 3 4 5 later years

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CF 4 4 4 6 6 g=4%

a. What are the deflated numbers corresponding to the above numbers?

b. If the appropriate deflated discount rate is 11%, what is the present value of those expected cash flows? Use all deflated numbers for your calculations.

c. Now use inflated numbers to calculate the present value.

What equations do I need to solve this step by step. I am completely lost here....

Answer 1

1.
Deflated Numbers=Inflated Numbers/(1+inflation)^t

CF1:
=4/1.025=3.90243902439024

CF2:
=4/1.025^2=3.80725758477097

CF3:
=4/1.025^3=3.714397643679

CF4:
=6/1.025^4=5.43570386879853

CF5:
=6/1.025^5=5.3031257256571

2.
Horizon Value=Cash flow in last year where growth becomes constant*(1+growth rate)/(1+inflation rate)/(discount rate-(1+growth rate)/(1+inflation rate)+1)=5.3031257256571*1.04*1/1.025*1/(11%-(1+4%)/(1+2.5%)+1)=56.42200

Present Value=Sum(Deflated Numbers/(1+deflated discount rate)^n)+Horizon Value/(1+deflated disount rate)^n
=3.90243902439024/1.11+3.80725758477097/1.11^2+3.714397643679/1.11^3+5.43570386879853/1.11^4+5.3031257256571/1.11^5+56.42200/1.11^5
=49.53323

3.
Inflated Discount rate=(1+deflated discount rate)*(1+inflation rate)-1=(1+11%)*(1+2.5%)-1=13.775%

Horizon Value=Cash flow in last year where growth becomes constant*(1+growth rate)/(discount rate-growth rate)=6*1.04/(13.775%-4%)=63.83632

Present Value=Sum(Inflated Numbers/(1+inflated discount rate)^n)+Horizon Value/(1+inflated disount rate)^n
=4/1.13775+4/1.13775^2+4/1.13775^3+6/1.13775^4+6/1.13775^5+63.83632/1.13775^5
=49.53323