Question

In need of assistance with Uniform Annual Worth and how number 5 should be solved.

4 What is the (simple) payback period for a project with the following characteristics? What is the uniform annual worth of the ten-year project? $27,000 $8000/yr $1000 in year 1, then increasing by $500/year annually 10 years First cost Annual benefits Annual maintenance Useful life Salvage value 10 years $2000 2000 afeo.1-527000+ $1000 ะ-$20,000 po2-2000D-5500+57000-3,500 4-(-52000 ear 3:-$13,500-$1000+$7000$7s00 4 $3000-(-3200o) 53000 o5:-32000-$2000+$7000 $3000 $5000 $soo0 $21002 $2ooly 0yrs A-52700+7000-350ot 3200 A- 4000 e k period with interest for the previous problem? What is If the MARR is 4%, what is the paybac the payback period with interest at a MARR of 18%? Fes2000 (5) lO GESS00 P-327000 1.0400 Yeon!:-527000倍4%, l)-57000+ $2000(4,4%, l)--si9080 04922 0.4902 0.3203 0.9739 0.2353 INSIO 3-$4678 t-3 (-54678) SS29S yenl-S27000俸15%y) t $1000+52000(#15%):本22860 Yeon 2 :-322860 t $ר 000+ S2000(9,18%,2.)-ssm@ ,15%2):-$1$(72 1.18 Q27ๆๆ 0.3902 12947 0.1917 01318 6128 (t: o $ 873 S-9 (873)-(-53061)

Answer 1

Solution 4
The payback period is the time required to earn back the amount invested in an asset from its net cash flows. It is a simple way to evaluate the risk associated with a proposed project. An investment with a shorter payback period is considered to be better, since the investor's initial outlay is at risk for a shorter period of time. The calculation used to derive the payback period is called the payback method.
Year	First Cost/ Initial Investment	Annual Benefits per year	Annual Maintenance	Net Cash inflows	Cummulative Net Cash Flows
1	27,000	8,000	1,000	7,000	7,000
2		8,000	1,500	6,500	13,500
3		8,000	2,000	6,000	19,500
4		8,000	2,500	5,500	25,000
5		8,000	3,000	5,000	30,000
		Payback period (in years)	4.40
		(4 Years+1 yearX2000/5000)
Solution 5
The discounted payback period is a capital budgeting procedure used to determine the profitability of a project. A discounted payback period gives the number of years it takes to break even from undertaking the initial expenditure, by discounting future cash flows and recognizing the time value of money.
If MARR is 4%
Year	First Cost/ Initial Investment	Annual Benefits per year	Annual Maintenance	Net Cash inflows	P.v.f @ 4%	Present Value of Net cash flows	Cumulative Net Cash Flows
1	27,000	8,000	1,000	7,000	0.9615	6,731	6,731
2		8,000	1,500	6,500	0.9246	6,010	12,740
3		8,000	2,000	6,000	0.8890	5,334	18,074
4		8,000	2,500	5,500	0.8548	4,701	22,776
5		8,000	3,000	5,000	0.8219	4,110	26,885
6		8,000	3,500	4,500	0.7903	3,556	30,442
				Payback period (in years)	4.03
				(5 Years+1 yearX27000-26885/30442-26885)
If MARR is 18%
Year	First Cost/ Initial Investment	Annual Benefits per year	Annual Maintenance	Net Cash inflows	P.v.f @ 18%	Present Value of Net cash flows	Cumulative Net Cash Flows
1	27,000	8,000	1,000	7,000	0.8475	5,932	5,932
2		8,000	1,500	6,500	0.7182	4,668	10,600
3		8,000	2,000	6,000	0.6086	3,652	14,252
4		8,000	2,500	5,500	0.5158	2,837	17,089
5		8,000	3,000	5,000	0.4371	2,186	19,275
6		8,000	3,500	4,500	0.3704	1,667	20,942
7		8,000	4,000	4,000	0.3139	1,256	22,197
8		8,000	4,500	3,500	0.2660	931	23,128
9		8,000	5,000	3,000	0.2255	676	23,805
10		10,000	5,500	4,500	0.1911	860	24,665
11		8,000	6,000	2,000	0.1619	324	24,988
12		8,000	6,500	1,500	0.1372	206	25,194
13		8,000	7,000	1,000	0.1163	116	25,310
14		8,000	7,500	500	0.0985	49	25,360
15		8,000	8,000	-	0.0835	-	25,360
Payback period is not possible in this case since at MARR 18%, the present value of all future net cash inflows would not be able to recover the initial cost due to increase in annual maintenance cost per year.