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4 questions · 1 formulas

Growing perpetuity

PV = CF1 / (r − g)

Trap: Use CF1, not CF0. Requires r > g.

DCF / NPV / IRRE-levelVery high priority

You are a rich student as usual, and therefore you will invest a small portion of your huge wealth in a Drisky office building in downtown San Fransico. You assume that the office building will generate annual cash flows forever (in perpetuity). One year from now, your investment will pay you $2 million. You also assume that the yearly payments will grow with a nice constant annual growth rate in perpetuity of 3% (g = 3%). The present value of the growing cash flow is $25 000 000. You assume that the risk- free rate of return (the risk-free discount rate) is 6%. Then the risk premia must be_____.

→ B) 5.00 %

Old Exam — Oct 2023, Q2

  • A) 5.24 %
  • B) 5.00 %
  • C) 11.24 %.
  • D) 11.00 %.
  • E) None of the above (A, B, C, D) is close to be correct.

Growing perpetuity: PV=CF1/(r-g). 25=2/(r-g) -> r-g=8%. Total required return r=11%. Risk premium =11%-6%=5% -> B.

Rule: Recognize cash-flow timing first. Discount each cash flow; terminal/sale proceeds are added in the sale year. IRR is the rate that sets NPV=0.

DCF / NPV / IRRE-levelVery high priority

You assume that your new investment will generate annual cash flow forever (in perpetuity). Today (now), your investment will pay you $1 million. Thereafter, you assume that the yearly payments grow with an incredible (according to you) constant annual growth rate in perpetuity. Your required rate of return (the discount rate) is 15%. The present value of the growing cash flow is $45 000 000. Then the constant annual growth rate must be_____.

→ A) 12.500 %

Old Exam — Dec 2021 re-exam, Q2

  • A) 12.500 %
  • B) 12.778 %
  • C) 2.500 %.
  • D) 13.5444 %.
  • E) None of the above (A, B, C, D) is close to be correct.

Payment today is 1m, then growing stream starts next year. 45 = 1 + [1(1+g)/(0.15-g)]. Solving gives g=12.5% -> A.

Rule: Recognize cash-flow timing first. Discount each cash flow; terminal/sale proceeds are added in the sale year. IRR is the rate that sets NPV=0.

DCF / NPV / IRRE-levelVery high priority

You assume that your new investment will generate annual cash flow forever (in perpetuity). Next year (year one) your investment will pay you $5 million. Thereafter, you assume that the yearly payments grow with an incredible (according to you) constant annual growth rate in perpetuity. Your required rate of return (the discount rate) is 12%. The present value of the growing cash flow is $62 500 000. Then the constant annual growth rate must be_____.

→ C) 4 %.

Old Exam — Oct 2021, Q2

  • A) 6 %
  • B) 5 %
  • C) 4 %.
  • D) 3 %.
  • E) None of the above (A, B, C, D) is close to be correct.

Growing perpetuity PV=CF1/(r-g): 62.5=5/(0.12-g) -> 0.12-g=0.08 -> g=4% -> C.

Rule: Recognize cash-flow timing first. Discount each cash flow; terminal/sale proceeds are added in the sale year. IRR is the rate that sets NPV=0.

DCF / NPV / IRRE-levelVery high priority

Income growth forever at g, CF1 known, required return r. Value?

→ B) CF1 / (r − g)

Formula Battle — method recognition (built from the Formula Book)

  • A) CF1 / r
  • B) CF1 / (r − g)
  • C) CF1 / (r + g)
  • D) CF0 / (r − g)

Growing perpetuity. Correct method: CF1 / (r − g).

Rule: PV = CF1/(r − g)