Question

the management of flasher is trying to decide whether to buy a new team of mules at a cost of $1.000 or a new tractor at a cost of $10.000 they will perform the same job but because the mules require more laborers the annual return ıs only $250 of net cash ınflows the tractor will return $2.000 of net cash ınflows per year the mules have a working life of 8 years and the tractor has aworking life of 10 years neither ınvestment is expected to have a salvage value at the end of its useful life flesher farms desired rate of return is %6 Should firm buy mules or tractor? Please compare 2 options based on NPV,IRR an Payback approaches.

Answer 1

NPV for a time period of n can be calculated using the formula: -C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return.

For Mules, NPV = -1000+250/1.06+250/1.06^2+...250/1.06^8

We can use present value of annuity formula for cashinflows which is P*(1-(1+r)^-n)/r

= -1000+ 250*(1-(1.06)^-8)/0.06

= -1000+1552.45

= 552.45

For Tractor, NPV=

-10000+2000/1.06+2000/1.06^2+....2000/1.06^10

= -10000+ 2000*(1-(1.06)^-10)/0.06

= -10000+14720.17

= 4720.17

As NPV of Tractor is greater than that of Mules, according to NPV, Firm should buy Tractor.

IRR is the discount rate at which NPV is 0.
Let IRR be r, then C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n= 0. Solving for r involves extensive trail and error. So, we can use a formula which is:
ra+ (NPVa/(NPVa-NPVb))*(Rb-Ra); where ra and rb are lower and higher discount rates and NPVa and NPVb are their corresponding NPV.

For Mules,

NPV is 552.45 at 6% discount rate. So, NPV will be 0 at higher discount rate. Consider a discount rate of 20% to calculate IRR. NPV at 20% will be -1000+250/1.2+250/1.2^2+...250/1.2^8= -40.71

Using the formula of IRR mentioned above, we get 6%+ (552.45/(552.45-(-40.71)))*(20%-6%)= 18.62%

For Tractor,

NPV is 4720.17 at 6%. So, NPV will be 0 at higher discount rate. Consider a discount rate of 20% to calculate IRR. NPV at 20% will be -10000+2000/1.2+2000/1.2^2+....2000/1.2^10= -1615.06
Using the formula of IRR mentioned above, we get 6%+ (4720.17/(4720.17-(-1615.06)))*(20%-6%)= 15.1%

As IRR of Mules is greater than Tractor, according to IRR, Firm should buy Mules.

Payback period is the period in which the cashinflows will cover the initial investment

For Mules, Payback period will be 4 years, as cumulative cashflow of 4 years is 1000, equal to initial investment.

For Tractor, Payback period will be 5 years, as cumulative cashflow of 5 years is 10000, equal to initial investment.

As Payback period of Mules is less than that of Tractor, according to payback period, Firm should buy Mules.

Though, the 3 criterias gave different results, Firm should go with NPV as decision based criteria, because the other two criterias has their own flaws. IRR has unrealistic assumption of reinvestment and Payback period doesnt gake into account time value of money.

So, Firm should buy Tractor by basing its decision on NPV.