Question

1. i) Your factory has been offered a contract to produce a part for a new printer. The contract would last for 33years and your cash flows from the contract would be $ 5.22 million per year. Your upfront setup costs to be ready to produce the part would be $7.86million. Your discount rate for this contract is 7.5%.

a) The NPV of the project is ____ millions (Round to two decimals)

(Also, SHOW HOW TO PUT IT IN THE TI-83 CALCULATOR)

ii) You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $4,700and will be posted for one year. You expect that it will generate additional revenue of $564 a month. What is the payback​period? (Round to one decimal) (Also, SHOW HOW TO PUT IT IN THE TI-83 CALCULATOR)

iii) You have been offered a unique investment opportunity. If you invest $11,200​today, you will receive $560 one year from​ now, $1,680 two years from​ now, and $11,200 ten years from now.

a. What is the NPV of the opportunity if the cost of capital is 5.4% per​ year? Should you take the​ opportunity?

b. What is the NPV of the opportunity if the cost of capital is 1.4%per​ year? Should you take it​ now?

Answer 1

Solution
	Question 1
		intial investments =$7.86 millions
		Contract is for (n) =33 years
		Per year inflow of cash from prinitng machine =$5.22 millions
		Disount rate is (r) =7.5%
		presnt value annuity factor =1/(1+r)^n
	Year	PVF @ 7.5%	Cash Flow	Presen value
		Initial outflow		-7.86
	1	0.930232558	5.22	4.855813953
	2	0.865332612	5.22	4.517036236
	3	0.80496057	5.22	4.201894173
	4	0.74880053	5.22	3.908738765
	5	0.696558632	5.22	3.636036061
	6	0.647961518	5.22	3.382359126
	7	0.602754901	5.22	3.146380583
	8	0.560702233	5.22	2.926865658
	9	0.521583473	5.22	2.722665729
	10	0.485193928	5.22	2.532712306
	11	0.451343189	5.22	2.356011447
	12	0.419854129	5.22	2.191638556
	13	0.390561981	5.22	2.03873354
	14	0.363313471	5.22	1.896496316
	15	0.337966019	5.22	1.76418262
	16	0.314386995	5.22	1.641100111
	17	0.292453018	5.22	1.526604755
	18	0.272049319	5.22	1.420097446
	19	0.253069134	5.22	1.32102088
	20	0.235413148	5.22	1.228856633
	21	0.218988975	5.22	1.143122449
	22	0.203710674	5.22	1.06336972
	23	0.189498302	5.22	0.989181135
	24	0.17627749	5.22	0.920168498
	25	0.16397906	5.22	0.855970696
	26	0.152538661	5.22	0.79625181
	27	0.141896429	5.22	0.740699358
	28	0.131996678	5.22	0.689022659
	29	0.122787607	5.22	0.64095131
	30	0.11422103	5.22	0.596233777
	31	0.106252121	5.22	0.554636072
	32	0.098839182	5.22	0.515940532
	33	0.091943425	5.22	0.479944681
			NPV	55.34073759
		Positive NPV means you can invest in project and buy a machine
	ii)
		Calculation of Payback period is
			payback period = inflow of cash / out flow of cash
			Inflow of cash = 564*12
				$6,768
			Now,
				=6768/4700
				1.44 years
	iii)	intial investments =$11200
		Contract is for (n) =10 years
		Disount rate is (r) =5.4% for caseA
		Disount rate is (r) =1.4% for case B
		presnt value annuity factor =1/(1+r)^n
		therei is two option lets make it case A & B
	Year	PVF @ 5.4%	Cash flow	Present value (pvf*cash flow)
	Initial cash flow	1	-11200	-11200
	1	0.948766603	560	531.3092979
	2	0.900158068	1680	1512.265554
	3	0.854039912		0
	4	0.810284547		0
	5	0.768770917		0
	6	0.729384172		0
	7	0.692015344		0
	8	0.656561047		0
	9	0.622923195		0
	10	0.591008723	11200	6619.297703
			NPV	-2537.127446
		IN case A NPV is negative hence investment is not beneficial
	For case B
	Year	PVF @ 5.4%	Cash flow	Present value (pvf*cash flow)
	Initial cash flow	1	-11200	-11200
	1	0.986193294	560	552.2682446
	2	0.972577213	1680	1633.929718
	3	0.959149125		0
	4	0.945906435		0
	5	0.932846583		0
	6	0.919967044		0
	7	0.90726533		0
	8	0.894738984		0
	9	0.882385586		0
	10	0.870202747	11200	9746.270769
			NPV	732.4687312
		IN case B NPV is positive hence investment is beneficial