Question

Drew owns and operates an onion packing plant. To bag and transfer the bags to pallets, Drew has two options. He can invest in a fully automatic bagging machine and palletizing machine or he can have partially automated baggers and have workers place the bags onto the pallets. The first option is a higher initial investment but has significant labor-cost savings.   The second option is a lower investment but has higher labor costs over the long run. After laying out the cash flows, Drew has determined that the fully automatic process has a NPV of $168,839.76 over 10 years.   The more labor intensive option has a NPV of $129,010.90 over 7 years. Drew's required rate of return is 10%, the inflation rate is 1%, the risk premium is 1% and the marginal tax rate is 30%.

1. What is the Real Discount Rate?

a.6.27%

b.5.29%

c.6.63%

d.6.75%

2. What is the annuity equivalent for the fully automatic bagging machine and palletizing machine?

a.$12,583.60

b.$25,243.07

c.$22,383.79

d.$23,633.53

3. What is the annuity equivalent for the partially automated baggers with workers placing the bags on pallets?

a.$18,380.24

b.$15,367.78

c.$12,758.23

d.$23,633.53

4. If Drew makes his decision based on the Annuity Equivalents, which should he choose?

a.fully automatic bagging machine and palletizing machine

b.partially automated baggers with workers placing the bags on pallets

c.Indifferent between the two

Answer 1

Summary of the information provided in the question are:

	fully automatic bagging machine	partially automated bagging machine
NPV	$ 168,839.76	$ 129,010.90
Usefullife (in years)	10	7
equired rate of return	10%
inflation rate is	1%
the risk premium is 1%	1%
the marginal tax rate is 30%.	30%

• When projects have different useful life NPV method cannot be used for economic decision making because its but natural that project with long life will have more period to make business where as short term one will have less period hence earning over the useful life will become imcopareable hence NPV method cannot be used.
• in such scenerio EAA - Equivalent Annual Annuity method is used as it compute annual annuitized return
  • Formual FOR EAA = (r x NPV) / (1-(1+r)^-n)
  • where,....
  • R = real discont rate of return
  • NPV = net present value
  • n= useful life

1. What is the Real Discount Rate?

Real discout rate = ({1+ [(required rate of return + risk premium) X (1-tax rate)]} / {1+inflation rate} ) - 1

Real discout rate = ({1+ [(10% + 1%) x (1-30%) ] } / { 1+1%} ) - 1

Real discout rate = ({1+ [(11%) x (70%) ] } / { 1+1%} ) - 1

Real discout rate = ({1+ 7.7%} / { 1+1%} ) - 1

Real discout rate = (1.077 / 1.01 ) - 1

Real discout rate = (1.06634 ) - 1

Real discout rate = 0.06634 x 100

Real discout rate = 6.63%

Hence correct option is : c : 6.63%

2. What is the annuity equivalent for the fully automatic bagging machine and palletizing machine?

EAA = (r x NPV) / (1-(1+r)^-n)

EAA = (6.63% x  $168,839.76) / (1-(1+6.63%)^-10)

EAA =11200.26 / (1-0.52606)

EAA =11200.26 / 0.4739

EAA =23633.53 (answer as per excel formula and rounded off)

Hence correct option is : d : 23633.53

3. What is the annuity equivalent for the Partial automatic bagging machine ?

EAA = (r x NPV) / (1-(1+r)^-n)

EAA = (6.63% x  $129,010.90) / (1-(1+6.63%)^-07)

EAA =8558.1488/ (1-0.63786)

EAA =8558.1488 / 0.3621

EAA =23633.53 (answer as per excel formula and rounded off)

Hence correct option is : d : 23633.53

4. If Drew makes his decision based on the Annuity Equivalents, which should he choose?

Project with higher EAA should be choosen but in this as case as EAA is same any project can be slected has both will have same economic benefits.

Hence......

Answer is option c. Indifferent between the two as botgh have same EAA