Question

In: Finance

Given the following two projects and their cash​ flows, ​, calculate the discounted payback period with...

Given the following two projects and their cash​ flows,

​, calculate the discounted payback period with a discount rate of 6%, 8​%,and 18​%.

What do you notice about the payback period as the discount rate​ rises? Explain this relationship.

With a discount rate of 6​%,

the cash outflow for project A​ is: 

A. recovered in 5 years.

B.recovered in 3.16 years.

C.recovered in 3 years.

D.never fully recovered.

 Cash Flow

A

B

  Cost

​ $8,000

​$100,000

  Cash flow year 1

​$2,857

​$10,000

  Cash flow year 2

​$2,857

​$20,000

  Cash flow year 3

​$2,857

​$30,000

  Cash flow year 4

​$2,857

​$40,000

  Cash flow year 5

​$2,857

​$15,000

  Cash flow year 6

​$2,857

​$0

Solutions

Expert Solution

Using excel formula to calculate discounted pay back period

Year 0.00 1 2 3 4 5 6
Project A Disount Rate =6% -8000 2857 2857 2857 2857 2857 2857
Discounted Cash Flow -8000.00 2695.28 2542.72 2398.79 2263.01 2134.92 2014.07
Cumulative Cash flow -8000.00 -5304.72 -2762.00 -363.20 1899.81 4034.72 6048.80
Discounted Payback Period 3.16
excel formula (=3-363.20/2263.01)
Year 0.00 1 2 3 4 5 6
Project A Disount Rate =8% -8000 2857 2857 2857 2857 2857 2857
Discounted Cash Flow -8000.00 2645.37 2449.42 2267.98 2099.98 1944.43 1800.39
Cumulative Cash flow -8000.00 -5354.63 -2905.21 -637.23 1462.75 3407.17 5207.57
Discounted Payback Period 3.30
excel formula (=3+637.23/2099.98)
Year 0.00 1 2 3 4 5 6
Project A Disount Rate =18% -8000 2857 2857 2857 2857 2857 2857
Discounted Cash Flow -8000.00 2421.19 2051.85 1738.86 1473.61 1248.82 1058.32
Cumulative Cash flow -8000.00 -5578.81 -3526.96 -1788.10 -314.49 934.33 1992.65
Discounted Payback Period 4.25
excel formula (4+314.49/1248.82)
Year 0.00 1 2 3 4 5 6
Project B Discount Rate =6% -100000 10000 20000 30000 40000 15000 0
Discounted Cash Flow -100000.00 9433.96 17799.93 25188.58 31683.75 11208.87 0.00
Cumulative Cash flow -100000.00 -90566.04 -72766.11 -47577.53 -15893.78 -4684.91 -4684.91
Discounted Payback Period Never Recovered
excel formula
Year 0.00 1 2 3 4 5 6
Project B Discount Rate =8% -100000 10000 20000 30000 40000 15000 0
Discounted Cash Flow -100000.00 9259.26 17146.78 23814.97 29401.19 10208.75 0.00
Cumulative Cash flow -100000.00 -90740.74 -73593.96 -49779.00 -20377.80 -10169.06 -10169.06
Discounted Payback Period Never Recovered
excel formula
Year 0.00 1 2 3 4 5 6
Project B Discount Rate =18% -100000 10000 20000 30000 40000 15000 0
Discounted Cash Flow -100000.00 8474.58 14363.69 18258.93 20631.56 6556.64 0.00
Cumulative Cash flow -100000.00 -91525.42 -77161.74 -58902.81 -38271.25 -31714.62 -31714.62
Discounted Payback Period Never Recovered
excel formula

At 6% Project A would be recovered in 3.16 years (Option b is correct option)


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