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FIN222Week7_TCH8:RQ3,5P6,9,10(a),16,23,25,26,31(9Questions,16parts) RQ 3 What is the intuition behind the paybac payback k rule? What are some of its drawb awbacks? acks? The payback period is the amount of time it takes for a project to pay back the initial investment. The drawbacks of the payback period are:  It does not adjust cash flows for time value of money  It ignores all cash flows beyond the payback period  The choice of the cut-off payback period is not grounded in economic theory  RQ5 Under what conditions will the IRR rule and the NPV rule give the same accept/reject decision?  For independent projects,  The investments under consideration are INDEPENDENT.  When evaluating independent projects, you would evaluate each project in isolation NOT in comparison to another. Therefore,  When evaluating a project in isolation, NPV > 0 (NPV cross-over point (i.e. one unique discount rate where NPVA=NPVB), The results of NPV and IRR will agree.  P6 Joyce Richardson owns her own business and is considering an investment. If she undertakes the investment, it will pay $4000 at the end of each of the next three years. The opportunity requires an initial investment of $1000 plus an additional investment at the end of the second year of $5000. What is the NPV of this opportunity if the cost of capital is 2% per year? Should Joyce take it? 0

1

2

3

–1000

4000

4000

4000

-5000

NPV   1,000 

4000 1000 4,000    $5729.69 1.02 1.022 1.023

Yes. Joyce should take it as NPV > 0.  Page 1 of 9 

P9

 John Howard reportedly was paid $400 000 to write his book Lazarus Rising. The book took three years to write. In the time he spent writing, Howard could have been paid to make speeches. Given his significance as Australia’s second-longest serving prime minister, assume that he could earn $300 000 per year (paid at the end of the year) speaking instead of writing. Assume his cost of capital is 10% per year.

a.

What is the NPV of agreeing to write the book (ignoring any royalty payments)? 0

1

2

3

400,000 –300,000 –300,000 –300,000

NPV  400,000   b.

300,000  1  1   $346,056  0.1  1.13 

Not a good idea for John to write the book as it will decrease his wealth by $346,056. Assume that, once the book was finished, it was expected to generate royalties of $200 000 in the first year (paid at the end of the year) and these royalties were expected to decrease at a rate of 30% per year in perpetuity. What is the NPV of the book with the royalty payments? 0

1

2

3

400 –300 –300 –300

4

5

6

200 200(1 - 0.3) 200(1 - 0.3)2

PV3



First, calculate the PV of the royalties at year 3 using a growing perpetuity formula with g= -30%.

𝑃𝑉  

200,000  $500,000 0.1  󰇛0.3󰇜

Then bring Year 3 Cash flow (=PV3) back to Year 0.

PVroyalties  

500, 000  $375, 657 1.13

Now add this to the NPV from part (a). NPV = –346,056 + 375,657 = $29,601



By agreeing to write the book including royalties, his wealth will increase by $29,601. Therefore John should only undertake the project subject to receiving the royalties. Page 2 of 9



P10  Superfast Bikes is thinking of developing a new composite road bike. Development will take six years and the cost is $200 000 per year. Once in production, the bike is expected to make $300 000 per year for 10 years. The cash inflows begin at the end of year 7. Assume that the cost of capital is 10%. Timeline: 0

1

2

3

-200,000 -200,000 -200,000

6

7

-200,000 300,000

16

300,000

PV6

PV= PV (annuity) + PV (Deferred annuity)

a.

Calculate the NPV of this investment opportunity. Should the company make the investment?

 300, 000  1  1  1.110 200, 000  1   0.1  NPV   1   0.1 1.16   1.16   

    $169, 482   

Invest as NPV > 0. 16. 

Professor Susan Jones has been offered the following deal: a law firm would like to retain her for an up-front payment of $50 000.



In return, for the next year the firm would have access to eight hours of her time every month. Jones’s rate is $550 per hour and her opportunity cost of capital is 15% per year.



What does the IRR rule advise regarding this opportunity? What about the NPV rule? o The cash flows are an immediate $50,000 cash flow followed by an annuity of $4400 per month (=8*$550) and a discount rate of 15% per year. 0

1

2

12

50,000

–4400

–4400

–4400

𝑁𝑃𝑉  50,000 

4400 1 1    1251.0 0.15 0.15  󰇡1  󰇢 12 12

Page 3 of 9 

o NPV > 0, therefore accept the deal. 23

   

You are considering making a movie. The movie is expected to cost $10 million up-front and take a year to make. After that, it is expected to make $5 million in the year it is released and $2 million for the following four years.  What is the payback period of this investment? If you require a payback period of two years, will you make the movie?  Does the movie have positive NPV if the cost of capital is 10%?

Timeline:



0

1

2

3

4

5

6

–10

0

5

2

2

2

2

It will take 4.5 years to pay back the initial investment, so the payback period is 4.5 years. You will not

2mil  1 1 4 0.1  1.1 5mil  make the movie. NPV   10mil   2 2 1.1  1.1

   

  $628,322 

NPV...