# Corporate Finance: Cost of Capital Part I – The Risk-less Rate

##### The cost of capital, or weighted average cost of capital, is probably the single most important number in corporate finance. It underpins many of the calculations you may be called upon to undertake. It is therefore important to know how to calculate it. Please watch all the videos in the series to get the full picture.

Hi there in one of my earliest discussions an episode on future value i mentioned that time value of money is the first basic principle of finance to the flesh the essence of the time value of money concept is that a dollar today is worth more than a dollar in the future if you have the dollar today you can invest it and earn a return on it so that on any future

Date you will have more than a dollar this is the future value of the dollar if you consider investing it for several periods and in successive periods expected to end returns then this process of calculating future value is called compounding because it includes earning returns on returns in every period you are earning a return not just on your original investment

But also on all the returns you have earned until then this process can also be undertaken in reverse assume that instead of asking what a certain amount of money today will be equal to at some point in the future we ask what a certain amount of money in the future is equal to today we then must reverse the calculations the process of calculating present value

Is called discounting which is the inverse of compounding this also involves earning a return on return although it is not easy to see it here as it was in the case of compounding calculating present and future values can also be viewed as the process of moving an amount of money forward or backwards through time the amount of money involved are called cash

Flows because they involve cash as opposed to some accounting measures like earnings it is easy to see that if we are anticipating several cash flows over time we can calculate the present value of each and then add them together to get the total present value of all cash flows here are the key points to keep in mind about calculating present and future values

And doing time value of money problems one the time value of money concept applies only to cash flows because we can earn returns or must pay return terms only on cash we invest upon we cannot calculate future values or present values for net income operating income and so on because they do not represent cash two we use the term compounding when we calculate

Future values or move earlier cash flows to a later point in time and the time discounting when we calculate present values or move cash flows to an earlier point in time however we often use the term discount rate to refer to the rates of return in both cases three the most important thing to remember about the discount rate you choose to apply to one or a series

See also  Bank of America success story | American multinational financial services company | Brian Moynihan

Of cash flows is that it must reflect the risk of the cash flow cash flows it is easy to understand that the discount rate should be higher for more risky cash flows or lower for less risky cash flows however estimating the risk of a cash flow and deciding what the appropriate discount rate for it should be is one of the naughtiest problems in finance for the

Rate at which you discount cash flows is known as the cost of capital or to give it its full name the weighted average cost of capital this is probably the single most important number in corporate finance as it underpins many of the calculations you may be called upon to perform although in many large corporates the cost of capital known as the header rate is

Given by head office to the divisions it is important for a financial analyst to know how to calculate it you may never be called a point to calculate it but it is helpful to know where it comes from and if one day you rise to be cfo it will be your role to determine the cost of capital of your fair and give it to the divisions so how do you calculate the cost

Of capital this is the topic of our discussion today but because it’s long and involved i shall break it down to several episodes before i continue however do visit our website where i create news and publications from international financial organizations and well central banks topics cover a wide range of financial and economic issues that affect individual

Countries or the world economy for instance covid-19 inflation or the war in ukraine please also subscribe to this channel and be informed whenever we publish a new video firms raise money from both equity investors and lenders to fund investments the cost of capital therefore is calculated as a weighted average of these sources of funding depending dependent on

The capital structure of the target firm most of risk and return modules in finance start off with an asset that is defined as risk-free and use the expected return on that asset as the risk-free rate the expected returns on risky investments are then measured relative to the risk-free rate but what makes an asset risk and what do we do when we cannot find such

An asset these are the questions we will deal with next an asset is risk-free if we know the expected returns on it with certainty that is the actual intent is always equal to the expected return under what conditions will the actual returns on an investment be equal to the expected returns there are two basic conditions that must be met the first is that there

Can be no default risk essentially this rules out any security issued by a private firm since even the largest and safest firms have some measure of default risk the only security is not at the chance of being on this free are government securities not because governments are better than corporations but because they control the printing of currency at least in

Nominal terms they should be able to fulfill their promises even this assumption straightforward though it might seem does not always hold up especially when governments refuse to honor claims made by previous regimes and when they borrow in currencies other than their own there is a second condition that respects securities need to fulfill that is often forgotten

For an investment to have actual return to equal it’s expected return there can be no reinvestment risk in most developed markets where the government can be viewed as a default free entity at least when it comes to borrowing in the local currency the implications are simple when doing investment analysis on longer term projects or valuations the risk for an age

Should be the long-term government bond rate if the analysis is short-term the short-term government security rate can be used as the risk-free rate the choice of a risk-free rate also has implications for how risk premiers are estimated if as is often the case historical these premiums are used where the access return and by stocks over and above a government

Security rate over a past period is used as the risk premium the government’s security chosen must be the same one as that used for the risk-free rate thus the historical risk premium used in the u.s should be the access return earned by stocks over treasury bonds and not treasury bills for purposes of long-term analysis the risk-free rate used to come up with

Expected returns should be measured consistently with how the cash flows are measured as if cash flows are estimated in nominal us dollar terms the risk-free rate will be the u.s treasury bond rate this also implies that it is not where fm is domicile that determines the choice of a risk-free rate but the currency in which the cash flows on the firm are estimated

Thus nestle can be valued using cash flows estimated in swiss francs discounted back at an expected return estimated using a swiss long-term government bond rate or it can be valued in british pounds with both the cash flows and the risk for the rate being in british pounds given that the same firm can be valued in different currencies will their results always be

Consistent if we assume purchasing power parity then differences in interest rate reflect differences in expected inflation both the cash flows and the discount rates are affected by expected inflation thus a low discount rate arising from a low risk free rate will be exactly offset by a decline in expected nominal growth rates for cash flows and the value will

Remain unchanged if the difference in interest rates across two currencies does not adequately reflect the differences in expected inflation in these currencies the values obtained using different currencies can be different firms will be valued more highly when the currency used is the one with low interest rates relative to inflation the risk however is that

The interest rates will have to rise at some point to correct for these divergence at which point the values will also converge under conditions of high and unstable inflation valuation is often done in real terms effectively this means that cash flows are estimated using real growth rate and without allowing for the growth that comes from price inflation to

Be consistent the discount rates used in these cases must prevail discount rate to get a real expected rate of return we need to start with a risk-free rate in real terms while government bills and bonds offer returns that are risk-free nominal terms they are not riskly in real terms since expected inflation can be volatile the standard approach of subtracting

And expecting an expected inflation rate from the nominal interest rate to arrive at a real risk frame rate provide at best and estimate of the real risk relate our discussion here too has been predicated on the assumption that governments do not default at least on local boroughly there are however many emerging market economies where this assumption might

Not be viewed as reasonable governments in these markets are perceived as capable of defaulting even on local border when this is coupled with the fact that many governments do not borrow long term locally there are scenarios where obtaining a local risk-free rate especially for the long term becomes difficult under these cases there are compromises that give

Us reasonable estimates of the risk-free rate one look at the largest and safest firms in that market and use the rates that they pay on their long-term borrowings in the local currency as a base given that these firms despite their size and stability still have default risk you would use a rate that is marginally lower than the corporate borrowing rate two if

There are long-term dollar denominated forward contracts on the currency you can use interest rate parity and the treasury bond rate or riskness rate in any other base currency to arrive at an estimate of the local borrowing rate i shall end here today next time i shall discuss the cost of equity

Transcribed from video
Corporate Finance: Cost of Capital Part I – The Risk-less Rate By Mike’s Economic Affairs