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ACCA FM · Guided practice (Show me how)

Chapter 7: Investment appraisal – methods

Annuities and perpetuities, immediate and deferred

(a) First proposal. A machine will cost $45,000 and is expected to generate $8,000 for each of the following 8 years. The cost of capital is 15% p.a. Calculate the NPV of the investment. (Annuity factor at 15%, years 1 to 8: 4.487.)

(b) Second proposal. The cost of capital is 12% p.a. What is the present value of $20,000 first receivable in 4 years' time and thereafter each year for a total of 10 years? (Annuity factors at 12%: years 1 to 3: 2.402; 1 to 4: 3.037; 1 to 10: 5.650; 1 to 13: 6.424.)

(c) Third proposal. A machine costs $100,000 and is expected to generate $12,000 p.a. in perpetuity. The cost of capital is 10% p.a. What is the NPV of the project?

(d) Fourth proposal. The rate of interest is 5% p.a. What is the present value of $18,000 first receivable in 5 years' time and thereafter annually in perpetuity? (Annuity factors at 5%: years 1 to 4: 3.546; 1 to 5: 4.329.)

The discount factor for a perpetuity (from year 1) is 1 / r.

  1. An annuity

    Calculate the machine's annuity present value and net present value for the first proposal.

  2. An annuity that starts later

    Calculate the deferred annuity factor and present value of the receipts for the second proposal.

  3. A perpetuity

    Calculate the perpetuity present value and net present value for the third proposal.

  4. A perpetuity that starts later

    Calculate the deferred perpetuity factor and present value of the receipts for the fourth proposal.

Opening this exercise…