Managerial Accounting - Capital Budgeting Exercises

Root Products is considering acquiring a manufacturing plant for $900,000$ .
The plant is expected to generate net cash inflows of $300,000$ annually and will need to be replaced in eight years.
The investment's payback period must occur before the replacement date for it to be profitable.
Payback Period = Investment Required / Annual Net Cash Inflow
Payback Period = 900,000 / $300,000 = 3 years
Decision: Root Products should purchase the plant since the payback period of 3 years is less than the 8-year replacement date.

Robinson Hardware is adding a new product line that requires an investment of $1,550,000$ .
The investment has a 10-year life and generates the following net cash inflows:
- Year 1: $330,000$
- Year 2: $275,000$
- Years 3-10: $250,000$ per year
The investment has no residual value.
Calculate the payback period:
- Cumulative inflow after Year 1: $330,000$
- Cumulative inflow after Year 2: 330,000 + $275,000 = $605,000
- Cumulative inflow after Year 3: 605,000 + $250,000 = $855,000
- Cumulative inflow after Year 4: 855,000 + $250,000 = $1,105,000
- Cumulative inflow after Year 5: 1,105,000 + $250,000 = $1,355,000
- Cumulative inflow after Year 6: 1,355,000 + $250,000 = $1,605,000
The investment is fully recovered during Year 6.
To find the exact payback period, calculate the fraction of Year 6 needed:
- Unrecovered investment after Year 5: 1,550,000 - $1,355,000 = $195,000
- Fraction of Year 6 needed: 195,000 / $250,000 = 0.78 years
Payback Period = 5 + 0.78 = 5.78 years

Robinson Hardware is adding a new product line requiring an investment of $1,550,000$ .
The investment has a 10-year life, generating net cash inflows as follows:
- Year 1: $330,000$
- Year 2: $275,000$
- Years 3-10: $250,000$ per year
The investment has no residual value.
Compute the Accounting Rate of Return (ARR):
- Total Net Cash Inflow = $2,605,000$
- Depreciation = (Investment - Residual Value) / Useful Life = (1,550,000 - $0) / 10 = $155,000 per year
- Average Net Income = (Total Net Cash Inflow - Total Depreciation) / Useful Life
- Total Depreciation = 155,000 * 10 = $1,550,000
- Average Net Income = (2,605,000 - $1,550,000) / 10 = $105,500
- ARR = (Average Net Income / Initial Investment) * 100
- ARR = (105,500 / $1,550,000) * 100 = 6.81

Star Golf Products is considering upgrading equipment with two options:
- Heatherwood Inc.: Cost = $900,000$ , Life = 6 years, Residual Value = $0, Annual Operating Income = $153,000
- Riverland Limited: Cost = $1,350,000$ , Life = 7 years, Residual Value = $100,000, Annual Operating Income = $249,750
Calculate the ARR for each option:
- Heatherwood Inc.:
  - Depreciation = (900,000 - $0) / 6 = $150,000 per year
  - ARR = (153,000 / $900,000) * 100 = 17
- Riverland Limited:
  - Depreciation = (1,350,000 - $100,000) / 7 = $178,571.43
  - ARR = (249,750 / $1,350,000) * 100 = 18.5

Retirement planning at age 52 with two strategies:
- Option 1: Save $2,700$ /year for 25 years (age 27-52), earning 10% annually.
- Option 2: Save $4,500$ /year for 15 years (age 37-52), earning 10% annually.
1. Out-of-pocket cash investment:
- Option 1: 2,700 * 25 = $67,500
- Option 2: 4,500 * 15 = $67,500
2. Accumulated savings at age 52:
- This requires future value of annuity calculations which are complex and depend on compounding.
3. Explanation:
- The results highlight the power of early investing due to compounding.
4. Investment value at age 62 (10 more years, no further investments):
- This requires calculating the future value of the lump sums accumulated at age 52 for another 10 years at 10%.

1. Invest $4,000$ at 10% per year. What will the investment be worth in six years?
- Future Value = Present Value * (1 + Interest Rate)^Number of Years
- Future Value = 4,000 * (1 + 0.10)^6 = $7,086.25
2. How much to invest now to withdraw $6,000$ at the end of every year for 20 years at 12% interest?
- This requires calculating the present value of an annuity.
3. Save $160,000$ in seven years at a 6% interest rate. How much do you need to invest now?
- Present Value = Future Value / (1 + Interest Rate)^Number of Years
- Present Value = 160,000 / (1 + 0.06)^7 = $106,274.13
4. Aunt Eugenia gives you $2,000$ at the end of every year for 10 years. Invest each gift at 12%. What will they be worth at the end of 10 years?
- This requires calculating the future value of an annuity.

Vargas Products is considering two projects:
- Project A: Cost = $280,000$ , Annual Net Cash Inflow = $56,000 for 8 years, Required Return = 16%
- Project B: Cost = $380,000$ , Annual Net Cash Inflow = $74,000 for 9 years, Required Return = 12%
NPV Calculation: NPV = Present Value of Cash Inflows - Initial Investment
Project A: NPV =
Project B: NPV =
What if Project B had a residual value of $60,000$ ? Add the present value of the residual value to the NPV calculation.

Walker Industries is deciding whether to automate a production process.
Equipment cost: $905,000$ , Life: 6 years
Projected net cash inflows:
- Year 1: $262,000$
- Year 2: $255,000$
- Year 3: $224,000$
- Year 4: $210,000$
- Year 5: $204,000$
- Year 6: $173,000$
Hurdle Rate: 14%
NPV Calculation:
- NPV = ∑ [Cash Inflow in Year t / (1 + Discount Rate)^t] - Initial Investment
- If NPV > 0, invest in the equipment.
- If NPV < 0, do not invest in the equipment.

Stanton Manufacturing is considering three capital investment proposals but can only pursue one.
Equipment A: Present Value of Net Cash Inflows = $1,710,000$ , Investment = $1,425,000, NPV = $285,000
Equipment B: Present Value of Net Cash Inflows = $1,950,000$ , Investment = $1,875,000, NPV = $75,000
Equipment C: Present Value of Net Cash Inflows = $2,180,000$ , Investment = $1,744,000, NPV = $436,000
Profitability Index = Present Value of Net Cash Inflows / Investment
- Equipment A: 1,710,000 / $1,425,000 = 1.20
- Equipment B: 1,950,000 / $1,875,000 = 1.04
- Equipment C: 2,180,000 / $1,744,000 = 1.25
Decision: Stanton Manufacturing should pursue Equipment C, as it has the highest profitability index, indicating the greatest return per dollar invested.