Question

(11) An investment project provides cash inflows of $765 per year for eight years. What is the project payback period if the initial cost is $2,400? What if the initial cost is $3,600? What if it is $6,500?

(12) An investment project has annual cash inflows of $4,200, $5,300, $6,100, and $7,400, and a discount rate of 14%. What is the discounted payback period for these cash flows if the initial cost is $7,000? What if the initial cost is $10,000? What if it is $13,000?

(13) A project that provides annual cash flows of $28,500 for nine years costs $138,000 today. Is this a good project if the required return is 8%? What if it’s 20%? At what discount rate would you be indifferent between accepting the project and rejecting it?

PLEASE SHOW ALL WORK PLEASE

Answer 1

Calculation of pay back period The future cash flows are in annuity. Hence- initial cost/annual cash flows (i) pay back period for initial cost $2400$2400/$ 765 3.137 or 3.14 years (ii) Pay back period for initial cost $36003600/$ 7654.705 or 4.71 years ii) pay back period for initial cost $6500 is difficult Here we need to consider total cash inflows for eight years - 8 years $ 765 $6120 If the initial cost is $ б500 the recovering the initial cost is not possible. if we use the formula like how we used before then the pay back period is: $6500/$ 765 8.49 or 8.50 years This above case is not possible as the cash flows stops after 8 years. Hence we can say there is no pay back period for initial cost $ 6500

Discounted Pay back period: we need to find the value of all cash flows today The project cash flows for the first four years. cash flow | preent value factor @ 14% | product 1$4200 1/1.14- 2 S5300 1/1.14*1.14- 3 $6100 1/1.14*1.14 1.140.67497 4117.317 4$7400 1/1.14*1.14 1.14 1.14-0.59208 4381.392 year 0.87719 3684.198 0.769474078.191 The discounted pay back period for initial cost $ 7000: discounted pay back period-1(7000- 3684.198)/4078.191] - 1+ 0.813 -1.813 years The discounted pay back period for initial cost $ 10000: discounted pay back period 2 (10000 - 3684.198-4078.191)/4117.317) - 2+0.543 -2.543 years (iiiThe discounted pay back period for initial cost $13000 discounted pay back period 3 (13000 - 3684.198-4078.191-4117.317)/4381.392] 3+ 0.255 - 3.255 years

The NPV of the project PV of the outflows - PV of the inflows Here the cash flows are in annuity, the equation for the NPV of this project is 8% required return (i) At 8 % Required Return : the equation is NPV--$ 138000 + $ 28500 ( PVIFA 896, 9 YEARS ) Hence at 8 % present value the NPV is positive. Therefore we can accept the project. At 20 % Required Reurn : the equation is = $40036.31 (ii) NPV :-$ 138000 + $ 28500 ( P VIFA 20% , 9 YEARS ) $23117.45 Hence at 20 % present value the NPV is Negative . Therefore we can Reject the project. (iii Indifferent for accepting and rejecting the project: We would be indifferent for accepting and rejecting the project if the Required return IRR Since at the Required return the NPV is zero $0 $138000+$28500 (PVIFA irr,9 years) IRR : 14.59%