This section provides more examples of how to evaluate the economic potential of an investment project based on ROR and NPV analysis. In the following example, the escalated dollar minimum ROR is assumed 15%, and the inflation rate will be 6%. As previously explained, Equation 52 can be applied to calculate the constant dollar minimum rate of return.
Example 54:
Calculate ROR for the investment that has the following projected today’s dollar costs and revenue:
C_{0}=$50,000  C_{1}=$80,000 
Rev_{2}=$100,000
OC_{2}=30,000 
Rev_{3}=$90,000
OC_{3}=30,000 
Rev_{4}=$80,000
OC_{4}=30,000 
L=0 


0  1  2  3  4 
C: Capital Cost, OC: Operating Cost, Rev: Revenue, L: Salvage
$\text{Presentvalueofallcosts=presentvalueofallrevenue}$$$\begin{array}{l}\text{Presentvalueofallcosts}={C}_{0}+\text{}{C}_{1}*\left(P/{F}_{i,1}\right)+O{C}_{2}*\left(P/{F}_{i,2}\right)+O{C}_{3}*\left(P/{F}_{i,3}\right)+OC4*\left(P/{F}_{i,4}\right)\\ =50,000+80,000*\left[1/{\left(1+i\right)}^{1}\right]+30,000*\left[1/{\left(1+i\right)}^{2}\right]+30,000*\left[1/{\left(1+i\right)}^{3}\right]+30,000*\left[1/{\left(1+i\right)}^{4}\right]\end{array}$$
$\begin{array}{l}\text{Presentvalueofallrevenues}=Re{v}_{2}*\left(P/{F}_{i,2}\right)+Re{v}_{3}*\left(P/{F}_{i,2}\right)\text{+}Re{v}_{4}*\left(P/{F}_{i,4}\right)\text{}\\ =100,000*\left[1/{\left(1+i\right)}^{2}\right]+90,000*\left[1/{\left(1+i\right)}^{3}\right]+80,000*\left[1/{\left(1+i\right)}^{4}\right]\end{array}$
$\begin{array}{l}50,000+80,000*\left[1/{\left(1+i\right)}^{1}\right]+30,000*\left[1/{\left(1+i\right)}^{2}\right]+30,000*\left[1/{\left(1+i\right)}^{3}\right]+30,000*\left[1/{\left(1+i\right)}^{4}\right]\\ =100,000*\left[1/{\left(1+i\right)}^{2}\right]+90,000*\left[1/{\left(1+i\right)}^{3}\right]+80,000*\left[1/{\left(1+i\right)}^{4}\right]0\\ =50,00080,000*\left[1/{\left(1+i\right)}^{1}\right]+70,000*\left[1/{\left(1+i\right)}^{2}\right]+60,000*\left[1/{\left(1+i\right)}^{3}\right]+50,000*\left[1/{\left(1+i\right)}^{4}\right]\end{array}$
So, ROR can be calculated as i = 15.61%.
Example 55:
Now, assume escalation rates of 8% per year for capital cost (development cost), 12% per year for operating costs and 10% per year for revenues. Calculate ROR and NPV for this investment, and make escalated dollar analysis considering 15% escalated dollar minimum rate of return, i*.
C_{0}=$50,000  C_{1}=$80,000*(F/P_{8%,1}) =86,400 
Rev_{2}=$100,000*(F/P_{10%,2}) =121,000 OC_{2}=30,000*(F/P_{12%,2}) =37,632 
Rev_{3}=$90,000*(F/P_{10%,3}) =119,790 OC_{3}=30,000*(F/P_{12%,3}) =42,148 
Rev_{4}=$80,000*(F/P_{10%,4}) =117,128 OC_{4}=30,000*(F/P_{12%,4}) =47,206 


0  1  2  3  4 
Present value of all costs = present value of all revenues
$$\begin{array}{l}\text{Presentvalueofallcosts}={C}_{0}+{C}_{1}*\left(P/F{}_{i,1}\right)+O{C}_{2}*\left(P/F{}_{i,2}\right)+O{C}_{3}*\left(P/F{}_{i,3}\right)+O{C}_{4}*\left(P/F{}_{i,4}\right)\text{}\\ =50,000+86,400*\left[1/\left(1+i\right)1\right]+37,632*\left[1/\left(1+i\right)2\right]+41,148*\left[1/\left(1+i\right)3\right]+47,206*\left[1/\left(1+i\right)4\right]\end{array}$$$$\begin{array}{l}\text{Presentvalueofallrevenues}=Re{v}_{2}*\left(P/{F}_{i,2}\right)+Re{v}_{3}*\left(P/{F}_{i,2}\right)+Re{v}_{4}*\left(P/F{}_{i,4}\right)\\ =121,000*\left[1/\left(1+i\right)2\right]+119,790*\left[1/\left(1+i\right)3\right]+117,128*\left[1/\left(1+i\right)4\right]\end{array}$$
$$\begin{array}{l}50,000+86,400*\left[1/\left(1+i\right)1\text{}\right]+37,632*\left[1/\left(1+i\right)2\right]+41,148*\left[1/\left(1+i\right)3\right]+47,206*\left[1/\left(1+i\right)4\right]\\ =121,000*\left[1/\left(1+i\right)2\right]+119,790*\left[1/\left(1+i\right)3\right]+117,128*\left[1/\left(1+i\right)4\right]\\ 0=50,00086,400*\left[1/\left(1+i\right)\text{}1\right]+83,368*\left[1/\left(1+i\right)2\text{}\right]+77,642*\left[1/\left(1+i\right)3\right]+69,922*\left[1/\left(1+i\right)4\right]\end{array}$$
Escalated dollar ROR for this project is calculated as: i=26.24%, and it is higher than 15% escalated dollar minimum rate of return, i*. So, the project is economically satisfactory.
$$\begin{array}{l}\text{NPV=Presentvalueofallcosts}\left(\text{15\%escalateddollarminimumrateofreturn}\right)\\ \text{+presentvalueofallrevenue}\left(\text{15\%escalateddollarminimumrateofreturn}\right)\end{array}$$$$\begin{array}{l}NPV=\text{}{C}_{0}{C}_{1}*\left(P/{F}_{15\%,1}\right)O{C}_{2}*\left(P/{F}_{15\%\text{},2}\right)O{C}_{3}*\left(P/{F}_{15\%,3}\right)O{C}_{4}*\left(P/{F}_{15\%\text{},4}\right)\\ +Re{v}_{2}*\left(P/F{}_{15\%}{}_{,2}\right)+Re{v}_{3}*\left(P/{F}_{15\%,2}\right)+Re{v}_{4}*\left(P/{F}_{15\%}{}_{,4}\right)\end{array}$$
$$\begin{array}{l}NPV=50,00086,400*\left[1/\left(1+0.15\text{}\right)1\right]37,632*\left[1/\left(1+\text{}0.15\right)2\right]41,148*\left[1/\left(1+\text{}0.15\text{}\right)3\right]\text{}\\ 47,206*\left[1/\left(1+\text{}0.15\text{}\right)4\right]+121,000*\left[1/\left(1+0.15\text{}\right)2\right]+119,790*\left[1/\left(1+\text{}0.15\text{}\right)3\right]+\\ 117,128*\left[1/\left(1+\text{}0.15\text{}\right)4\right]=\end{array}$$
$$\begin{array}{l}NPV=50,00086,400*\left[1/\left(1+\text{}0.15\text{}\right)1\right]+83,368*\left[1/\left(1+\text{}0.15\text{}\right)2\right]\\ +77,642*\left[1/\left(1+\text{}0.15\text{}\right)3\right]+69,922*\left[1/\left(1+\text{}0.15\text{}\right)4\right]=28,937\text{}dollars\end{array}$$
Since NPV at 15% escalated dollar minimum rate of return is positive, we can conclude that the project is economically satisfactory.
Example 56:
Now, consider inflation rate of 6% per year for Example 55 and make constant dollar analysis.
Constant dollar amounts can be calculated as:
C_{0}=$50,000  C_{1}=$86,400*(P/F_{6%,1}) = 81,509.43 
Rev_{2}=$83,368*(P/F_{6%,2}) = 74,197.22 
Rev_{3}=$77,642*(P/F_{6%,3}) = 65,189.85 
Rev_{4}=$69,922*(P/F_{6%,4}) = 55,385.11 


0  1  2  3  4 
ROR for this project is i=19.09%,
For constant dollar analysis, it is necessary to derive constant dollar minimum rate of return, i'*, from escalated dollar minimum rate of return, i*, and inflation rate applying equation 52.
$$\begin{array}{l}i\text{'}*=\left[\left(1+i*\right)/\left(1+f\right)\right]1\\ i\text{'}*=\left[\left(1+0.15\right)/\left(1+0.06\right)\right]1=0.0849=8.49\%\end{array}$$Therefore, the constant dollar minimum rate of return, i'*, will be 8.49%.
The constant dollar ROR for this project is calculated as 19.09%, and it is higher than i'* = 8.49%. So, the project is economically satisfactory.
In order to calculate the constant dollar NPV, we have to calculate it at a constant dollar minimum rate of return, i'*= 8.49%.
$$\begin{array}{l}NPV=50,00081,509.43*\left[1/\left(1+\text{}0.849\right)1\right]+74,197.22*\left[1/\left(1+\text{}0.\text{}849\right)2\right]\text{}\\ +65,189.85*\left[1/\left(1+0.\text{}849\right)3\right]+55,385.11*\left[1/\left(1+\text{}0.\text{}849\right)4\right]=\$28,937\text{}\end{array}$$Constant dollar NPV at i'*= 8.49% is positive, so, the project is economically satisfactory.
Please watch the following (17:17) video: Escalated and constant dollar ROR and NPV analysis
Summary of calculations:
 Step 1: Calculating escalated dollar cash flow using escalation rate and F/P factor
 Calculating escalated dollar ROR from calculated escalated dollar cash flow in step 1
 Calculating escalated dollar NPV from calculated escalated dollar cash flow in step 1 and given escalated dollar minimum rate of return, i*
 Step 2: Calculating constant dollar cash flow using the given inflation rate and P/F factor from the calculated escalated dollar cash flow in step 1
 Calculating constant dollar ROR from calculated constant dollar cash flow in step 2
 Calculating constant dollar minimum rate of return, i'*, from given escalated dollar minimum rate of return, i*, and given inflation rate, f, using Fisher equation
 Calculating constant dollar NPV from calculated constant dollar cash flow in step 2 and calculated constant dollar minimum rate of return, i'*
Note that the constant dollar NPV is identical to the escalated dollar NPV. Constant NPV equations are mathematically equivalent to escalated dollar NPV equations and then give the same results.
Note that Example 54 implicitly assumes the escalation rate is 0% per year. So, for NPV and ROR analysis in Example 54, we need to consider a 15% escalated dollar minimum rate of return.
$$\begin{array}{l}NPV\text{}=50,00080,000*\left[1/{\left(1+0.15\right)}^{1}\right]+70,000*\left[1/{\left(1+0.15\right)}^{2}\right]+\\ 60,000*\left[1/{\left(1+0.15\right)}^{3}\right]+50,000*\left[1/{\left(1+0.15\right)}^{4}\right]=1,403\end{array}$$And since it is positive, the project is economically satisfactory.
And calculated ROR (15.61%) is also higher than the 15% escalated dollar minimum rate of return, so we can conclude that the project is economically satisfactory.