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TEME is a manufacturer of toy construction equipment. If it pays out all of its earnings as dividends, it will have earnings of 0.3 million per quarter in perpetuity. Suppose that the discount rate, expressed as an effective annual rate (EAR), is 16%. TEME pays dividends quarterly. Suppose that TEME is considering a one-time expansion into toy xylophones. It is estimated that this will cost 1M. Assume that this cost will be incurred at the end of the year, one year from now. As a result of expansion, earnings in subsequent quarters (i.e. starting in 1 year and 1 quarter from now) would be 0.05 million higher than without the expansion. Calculate the value of TEME if it undertakes the investment.

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jepessoa

Answer:

$8.078 million

Explanation:

we must use the same time periods, so instead of using an annual discount rate, we should use a quarterly rate:

effective quarterly interest = (1 + 0.16)¹/⁴ - 1 = 0.0378 = 3.78%

dividends per quarter = 0.3 million + 0.05 million = $0.35 million

terminal value of firm in quarter 4 = 0.35 / 0.0378 = $9.26 million

present value of terminal value = $9.26 / (1.0378)⁴ = $7.983 million

present value of 4 quarterly dividends = $0.3 x 3.64879 (PVIFA, 3.78%, 4 periods) = $1.095 million

NPV = -$1 + $1.095 + $7.983 = $8.078 million

We must use the same time periods, so instead of using an annual discount rate, we should use a quarterly rate:  

  • Effective quarterly interest = (1 + 0.16)¹/⁴ - 1 = 0.0378 = 3.78%
  • Dividends per quarter = 0.3 million + 0.05 million = $0.35 million
  • Terminal value of firm in quarter 4 = 0.35 / 0.0378 = $9.26 million
  • Present value of terminal value = $9.26 / (1.0378)⁴ = $7.983 million
  • Present value of 4 quarterly dividends = $0.3 x 3.64879 (PVIFA, 3.78%, 4 periods) = $1.095 million
  • NPV = -$1 + $1.095 + $7.983 = $8.078 million

The value of TEME if it undertakes the investment is $8.078 million.

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