Future cash flows are our organisations’ lifeblood. We corporate treasurers must evaluate them correctly. Failures can be very expensive. Fundamental evaluation tools include discounting, annuity factors and perpetuities, both in growth and decline. Dealing properly with decline is a challenging calculation.

The value of cash flows depends on timing, as well as amount. The further in the future our cash flow, the smaller its present value (PV). We usually discount cash flows to PVs, to make them comparable. We discount single cash flows with discount factors (DF). The DF is a number less than one. Simply multiply the cash flow by the DF to work out the PV.

**DF = 1 / (1 + r)n** **r = cost of capital per period, for example 0.06** **n = number of periods’ maturity, for example 4** DFs reflect the timing of the cash flow, and the cost of capital for its maturity, driven in turn by the cash flow’s risk. **Example: four-period DF** **DF = 1 / (1+r)n** **= 1 / (1.06)4 = 0.79 (to the nearest 0.01)**

Many future cash flows are annuities. An annuity is a regular series of predictable cash flows, for example, interest on a bond. Simple annuities start exactly one period in the future, and continue at a fixed amount for a fixed number of future periods. Simple annuities can be valued using an annuity factor (AF).

**AF = (1 – DF) / r** **DF = discount factor for longest maturity** **r = cost of capital per period** An AF is the total of the DFs for each cash flow in the annuity when the cost of capital is the same for all maturities. Like DFs, AFs are driven by the timing of the final future cash flow, and the cost of capital, reflecting risk. **Example: four-period AF** **r = 0.06; n = 4** **DF = 0.79 (worked out before)** **AF = (1 – DF) / r** **= (1 – 0.79) / 0.06 = 3.5** The PV is the first cash flow multiplied by the AF. AFs have many other advanced applications. Examples include calculating and evaluating instalments for leases, hire purchase and loans. AFs will serve you faithfully throughout your career. Invest time to master them.

Follow this link for AF case studies and further resources on these topics.

**PV = first cash flow x 1 / (r – g)** **g = rate of growth/decline per period** When our modelled series of expected future cash flows is extended indefinitely, it is a perpetuity. Examples of fixed perpetuities include perpetual government bonds. We can make a very quick valuation of a mature business, in a relatively steady state, by modelling its cash flows as a growing or declining perpetuity. Growing and declining perpetuities are both valued with the same formula.

Future growth-rate assumptions are fundamentally important. Overestimating future growth can lead to substantial overvaluations, and overpaying for acquisitions.

Dealing correctly with negative growth (decline) can also be tricky. When future growth is negative, ‘g’ is negative. We deduct this negative number (g) from the cost of capital (r). Deducting negative numbers increases the cost of capital we started with, reducing the valuation. Follow this link for examples and applications of perpetuities.

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Develop practical skills and understanding with the help of ACT’s Nuts and Bolts of Cash Management training course.

**Doug Williamson FCT** is a treasury and finance coach

**This article was taken from the Feb/Mar issue of The Treasurer magazine. For more great insights, log in to view the full issue or sign up for eAffiliate membership**