Midterm practice, corporate finance.
Eight questions per paper, in the shape of the course homework. Pick a difficulty, type your answers, check them, and open the working when you are stuck. Regenerate gives you a new paper.
A cash flow that grows fast, then slowly
Kestrel Robotics can invest in a new product line. It costs $1,000 today and will bring in $100 at the end of the first year. That cash flow grows by 12% a year through year 10, then by 5% a year forever after. The discount rate is 15%.
- (a)
What is the present value today of the cash flows in years 1 to 10?
Years 1 to 10 are a growing annuity: 10 payments that start at $100 and grow by 12% a year.
PV = C/(r − g) × [1 − ((1 + g)/(1 + r))N]= 100/(0.15 − 0.12) × [1 − (1.12/1.15)10] = 3,333.33 × (1 − 0.76772) = 774.27The homework's way gives the same number: a growing perpetuity from year 1, worth 3,333.33, minus the same perpetuity started in year 11, worth 2,559.06 today (100 × 1.1210/(0.15 − 0.12), discounted 10 years). 3,333.33 − 2,559.06 = 774.27.Answer: $774.27 - (b)
What is the cash flow in year 11?
C11 = 100 × 1.129 × 1.05 = 277.31 × 1.05 = 291.17The year-10 cash flow has grown 9 times, not 10: the first year of fast growth is the starting amount.Answer: $291.17 - (c)
What is the value today of all the cash flows from year 11 on?
From year 11 the cash flow is a growing perpetuity. Its formula values it one year before its first payment: at year 10.
Value at year 10 = 291.17/(0.15 − 0.05) = 2,911.73PV today = 2,911.73/1.1510 = 719.74Answer: $719.74 - (d)
What is the project's NPV?
NPV = −1,000 + 774.27 + 719.74 = 494.01Answer: $494.01 - (e)
Should Kestrel Robotics invest?
Take a project when its NPV is above zero: taking it is like receiving the NPV in cash today.
Answer: Yes: the NPV is positive
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