Consider the following table consisting of the years and cash flows of two projects under appraisal.(use 10% discount rate whenever necessary?

year 0 1 2 3 4 5
project 1 40000 10000 20000 10000 18000 15000
project 2 40000 12000 18000 24000 15000 10000
A. the net present value (NPV) of the project and which project is the relevant project and why?
B.the payback period of the project and which project is the relevant project and why?
C.the discounted payback period of the project and which project is the best project and why?
D.the profitability index of the project and which project is the relevant project and why?
E. the net benefit cost ratio (nbcr) of the projectand which project is the relevant project and why?

1 answer

To evaluate the two projects by calculating the NPV, Payback Period, Discounted Payback Period, Profitability Index, and Net Benefit Cost Ratio (NBCR), we will use a discount rate of 10%.

First, let's compile the cash flows for both projects:

Cash Flows

| Year | Project 1 | Project 2 | |------|-----------|-----------| | 0 | 40000 | 40000 | | 1 | 10000 | 12000 | | 2 | 20000 | 18000 | | 3 | 10000 | 24000 | | 4 | 18000 | 15000 | | 5 | 15000 | 10000 |

A. Net Present Value (NPV)

NPV is calculated using the formula:

\[ NPV = \sum \left( \frac{CF_t}{(1 + r)^t} \right) - Initial , Investment \]

where \( CF_t \) is cash flow at time \( t \), \( r \) is the discount rate, and \( t \) is the year.

For Project 1:

\[ NPV = \frac{40000}{(1 + 0.10)^0} + \frac{10000}{(1 + 0.10)^1} + \frac{20000}{(1 + 0.10)^2} + \frac{10000}{(1 + 0.10)^3} + \frac{18000}{(1 + 0.10)^4} + \frac{15000}{(1 + 0.10)^5} - 40000 \]

\[ = 40000 + \frac{10000}{1.10} + \frac{20000}{1.21} + \frac{10000}{1.331} + \frac{18000}{1.4641} + \frac{15000}{1.61051} - 40000 \]

Calculating each term:

  • \( 40000 = 40000 \)
  • \( \frac{10000}{1.10} \approx 9090.91 \)
  • \( \frac{20000}{1.21} \approx 16528.93 \)
  • \( \frac{10000}{1.331} \approx 7513.15 \)
  • \( \frac{18000}{1.4641} \approx 12338.68 \)
  • \( \frac{15000}{1.61051} \approx 9307.63 \)

Summing these gives us:

\[ NPV \approx 40000 + 9090.91 + 16528.93 + 7513.15 + 12338.68 + 9307.63 - 40000 \] \[ NPV \approx 11370.295 \]

For Project 2:

\[ NPV = \frac{40000}{(1 + 0.10)^0} + \frac{12000}{(1 + 0.10)^1} + \frac{18000}{(1 + 0.10)^2} + \frac{24000}{(1 + 0.10)^3} + \frac{15000}{(1 + 0.10)^4} + \frac{10000}{(1 + 0.10)^5} - 40000 \]

Calculating each term:

  • \( 40000 = 40000 \)
  • \( \frac{12000}{1.10} \approx 10909.09 \)
  • \( \frac{18000}{1.21} \approx 14876.03 \)
  • \( \frac{24000}{1.331} \approx 18087.76 \)
  • \( \frac{15000}{1.4641} \approx 10243.33 \)
  • \( \frac{10000}{1.61051} \approx 6209.31 \)

Summing these gives us:

\[ NPV \approx 40000 + 10909.09 + 14876.03 + 18087.76 + 10243.33 + 6209.31 - 40000 \] \[ NPV \approx 14025.52 \]

Conclusion for A:

  • NPV of Project 1: \( 11370.295 \)
  • NPV of Project 2: \( 14025.52 \)

Relevant Project: Project 2, because it has a higher NPV.

B. Payback Period

The payback period is the time it takes for a project to recover its initial investment.

For Project 1:

  1. Year 0: -40000
  2. Year 1: -40000 + 10000 = -30000
  3. Year 2: -30000 + 20000 = -10000
  4. Year 3: -10000 + 10000 = 0

Payback period of Project 1: 3 years.

For Project 2:

  1. Year 0: -40000
  2. Year 1: -40000 + 12000 = -28000
  3. Year 2: -28000 + 18000 = -10000
  4. Year 3: -10000 + 24000 = 14000

Payback period of Project 2: 3 years (but slightly before end of year 3).

Conclusion for B:

  • Payback period of Project 1: 3 years
  • Payback period of Project 2: 2.8333 years

Relevant Project: Project 2, as it has a shorter payback period.

C. Discounted Payback Period

The discounted payback period accounts for the time value of money.

For Project 1:

  • Year 0 (40000): -40000
  • Year 1: 9090.91 => -30909.09
  • Year 2: 16528.93 => -14380.16
  • Year 3: 7513.15 => -6856.98
  • Year 4: 12338.68 => 3481.70 (Completed between year 4 and year 5)

Discounted payback period of Project 1: Between Year 4 and Year 5, approximately 4.5 years.

For Project 2:

  • Year 0 (40000): -40000
  • Year 1: 10909.09 => -29090.91
  • Year 2: 14876.03 => -14214.88
  • Year 3: 18087.76 => 3892.88 (Completed between year 3 and year 4)

Discounted payback period of Project 2: Between Year 3 and Year 4, approximately 3.5 years.

Conclusion for C:

  • Discounted payback period of Project 1: 4.5 years
  • Discounted payback period of Project 2: 3.5 years

Best Project: Project 2, as it has a shorter discounted payback period.

D. Profitability Index (PI)

The Profitability Index is calculated as:

\[ PI = \frac{NPV + Initial , Investment}{Initial , Investment} \]

For Project 1: \[ PI_1 = \frac{11370.295 + 40000}{40000} \approx 1.2843 \]

For Project 2: \[ PI_2 = \frac{14025.52 + 40000}{40000} \approx 1.3506 \]

Conclusion for D:

  • Profitability Index of Project 1: \( 1.2843 \)
  • Profitability Index of Project 2: \( 1.3506 \)

Relevant Project: Project 2, as it has a higher Profitability Index.

E. Net Benefit Cost Ratio (NBCR)

NBCR is calculated as:

\[ NBCR = \frac{Total , Present , Value , of , Cash , Flows}{Initial , Investment} \]

For Project 1:

\[ \text{Total Present Value of Cash Flows (Project 1)} \approx 51370.295 \] \[ NBCR_1 = \frac{51370.295}{40000} \approx 1.2843 \]

For Project 2:

\[ \text{Total Present Value of Cash Flows (Project 2)} \approx 54025.52 \] \[ NBCR_2 = \frac{54025.52}{40000} \approx 1.3506 \]

Conclusion for E:

  • NBCR of Project 1: \( 1.2843 \)
  • NBCR of Project 2: \( 1.3506 \)

Relevant Project: Project 2, as it has a higher NBCR.

Summary

  • NPV: Project 2 is better.
  • Payback Period: Project 2 is better.
  • Discounted Payback Period: Project 2 is better.
  • Profitability Index: Project 2 is better.
  • NBCR: Project 2 is better.

Overall, Project 2 is the superior choice based on all metrics calculated.