Equivalence of Real-Dollar and Actual-Dollar Cash Flows In Example 8-1 , your salary was projected to increase at the rate of 4% per year, and the general price inflation rate was expected to be 6% per year. Your resulting estimated salary for the four years in actual and real dollars was as follows : End of Year, k Salary (A$) Salary (R$), b = 1 1 45,000 45,000 2 46,800 44,151 3 48,672 43,318 4 50,619 42,500 What is the present worth (PW) of the four-year actual- and real-dollar salary cash flows at the end of year one (base year) if your personal MARR[latex]_{m}[/latex] is 10% per year (i[latex]_{m}[/latex])?

(a) Actual-dollar salary cash flow: PW(10%)1 = $45,000 + $46,800(P/F, 10%, 1) + $48,672(P/F, 10%, 2) + $50,619(P/F, 10%, 3) = $165,798. (b) Real-dollar salary cash flow: [latex]i_{r}=\frac{i_{m}-f}{1+f}= \frac{0.10 − 0.06}{1.06}[/latex]= 0.03774, or 3.774%; PW(3.774%)[latex]_{1}[/latex] = $45,000 + $44,151 [latex]\left(\frac{1}{1.03774} \right)^{1}[/latex] + $43,318[latex]\left(\frac{1}{1.03774} \right)^{2}[/latex] + $42,500 [latex]\left(\frac{1}{1.03774} \right)^{3}[/latex] = $165,798. Thus, we obtain the same PW at the end of year one (the base time period) for both the actual-dollar and real-dollar four-year salary cash flows when the appropriate interest rate is used for the equivalence calculations.

Question 8.5: Equivalence of Real-Dollar and Actual-Dollar Cash Flows In E...

Engineering Economy

Equivalence of Real-Dollar and Actual-Dollar Cash Flows

In Example 8-1, your salary was projected to increase at the rate of 4% per year, and the general price inflation rate was expected to be 6% per year. Your resulting estimated salary for the four years in actual and real dollars was as follows :

End of Year, k	Salary (A$)	Salary (R$), b = 1
1	45,000	45,000
2	46,800	44,151
3	48,672	43,318
4	50,619	42,500

What is the present worth (PW) of the four-year actual- and real-dollar salary cash flows at the end of year one (base year) if your personal MARR $_{m}$ is 10% per year (i $_{m}$ )?

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(a) Actual-dollar salary cash flow:
PW(10%)1 = $45,000 + $46,800(P/F, 10%, 1)
+ $48,672(P/F, 10%, 2) + $50,619(P/F, 10%, 3)
= $165,798.
(b) Real-dollar salary cash flow:

$i_{r}=\frac{i_{m}-f}{1+f}= \frac{0.10 − 0.06}{1.06}$ = 0.03774, or 3.774%;

PW(3.774%) $_{1}$ = $45,000 + $44,151 $\left(\frac{1}{1.03774} \right)^{1}$ + $43,318 $\left(\frac{1}{1.03774} \right)^{2}$ + $42,500 $\left(\frac{1}{1.03774} \right)^{3}$

= $165,798.
Thus, we obtain the same PW at the end of year one (the base time period) for both the actual-dollar and real-dollar four-year salary cash flows when the appropriate interest rate is used for the equivalence calculations.