Question

CHAPTER 8 Net Present Value and Other Investment Criteria 21. NPV and Payb exclusive projects a Payback Period. Kaleb Konstruction, Inc., has the following mutually S ects available. The company has historically used a three-year cutoff rojects. The required return is 10 percent. Year домо Project F -$150,000 78,000 54,000 68,000 60,000 54,000 Project G -$235,000 54,000 72,000 103,000 139,000 156,000 2. Calculate the payback period for both projects. b. Calculate the NPV for both projects. c. Which project, if any, should the company accept?

Answer 1

For payback We will calculate Cumulative cash flow  
NPV is sum of present value of all cash flows.  
Present value of cash flows = cash flows * PVF  
  
PVF formula = 1/(1+Discount rate)^period  
For year 1, PVF = 1/(1+10%)^1=   0.9090909091
For year 2, PVF = 1/(1+10%)^2=   0.826446281
and so on.  

Project F              
For payback We will calculate Cumulative cash flow              
   cash inflows   Cumulative cash inflows   PVF   Cash flows*PVF
year 0   -150000   -150000   1   -150000
Year 1   78000   -72000   0.9090909091   70909.09091
Year 2   54000   -18000   0.826446281   44628.09917
Year 3   68000   50000   0.7513148009   51089.40646
Year 4   60000   110000   0.6830134554   40980.80732
Year 5   54000   164000   0.6209213231   33529.75145
              
Sum   164000           91137.15531
Payback year = year before positive cumulative cash flow + (cumulative cash flow to make cum. cash flow to 0/Cash flow of first positive cumulative CF)              
   2 + (18000/68000)          
   2.264705882          
NPV is   $91,137.16   

payback period is =   2.26          

Explaination: in Year 3 cumulative cash flow is positive. It means Full cost is recovered between year 2 and year 3. In year 3 $497500 is required to fully recover the cost. While total cash flow is $1215000 during year 3. So in 2 years +(497500/1215000)= 2.4095 years, cost is fully recovered. .

Project G              
For payback We will calculate Cumulative cash flow              
   cash inflows   Cumulative cash inflows   PVF   Cash flows*PVF
year 0   -235000   -235000   1   -235000
Year 1   54000   -181000   0.9090909091   49090.90909
Year 2   72000   -109000   0.826446281   59504.13223
Year 3   103000   -6000   0.7513148009   77385.42449
Year 4   139000   133000   0.6830134554   94938.8703
Year 5   156000   289000   0.6209213231   96863.7264
              
Sum   289000           142783.0625
Payback year = year before positive cumulative cash flow + (cumulative cash flow to make cum. cash flow to 0/Cash flow of first positive cumulative CF)              
   3+ (6000/139000)          
   3.043165468          
NPV is   $142,783.06          
payback period is =   3.04          

NPV of both projects is positive. On the basis of higher NPV, project G is acceptable.

Payback cutoff is 3 years. Project G has 3.04 years payback, while project F is 2.26 years. On the basis of cutoff of payback, project F is acceptable.

Rationale will choose project G