FIN 320F unit 6

what happens to a FV if you increase the rate, r? what happens to a PV?

-FV: positively related to interest rates; the higher the interest rate, the higher the amount of interest earned each period; increased r will cause an increased value -PV: inversely related to interest rates; increased r will cause a decreased value

as you increase the length of time involved, what happens to FVs? and to PVs?

-FV: positively related to the length of time of the investment, as each additional period additional interest is earned -PV: inversely related to the length of time of the investment

Why would TMCC be willing to accept such a small amount ($24,099) in exchange for a promise to repay about 4x that amount ($100,000) in the future ?

-TMCC borrow money because it hopes to earn a higher rate of return in its capital budgeting protects than the rate payed to their creditors -the creditors lend $24,099 and receive $100k in 30 years they would earn an IRR of 4.86% -if TMCC takes the $24,099 and invests it wisely, it would earn more than 4.86% they pay to creditors -if the rate of return on TMCC's project was 6%, the borrowed $24,099 would grow to an inflow of $138,412 -after paying their debt, they would have $28,412 that they didn't have before

perpetuities

-a series of regular payments for regular periods that go on indefinitely -regular stream of cash flows that is indefinite-- goes on forever

as you increase the length of time involved, what happens to the PV value of an annuity? what about to the FV?

-assuming positive cash flows and a positive interest rate, both the PV and FV will rise -when you add an additional period to annuity, you're also adding an additional cash flows

let's say that when TMCC offered the security of $24,099, the US treasury had offered an essentially identical security. do you think it would have a higher or lower price? why?

-both offer a future payment of $100,000 in 30 years -the treasury security should be evaluated at the risk-free rate of return; the risky security should be evaluated at it's appropriate risk-adjusted opportunity cost -risky: 4.68% at $24,099 -to get this rate on an investment that will pay $100k with certainty that you would a expected a lower rate of return a pay a higher price -if the risk free rate is 1%, then the PV of the $100k would be: $100k/(1.01)^30= $74,192

A corporation wants to earn an effective annual return on its consumer loans of 14.2%. the bank uses daily compounding on loans. what interest rate is the bank required by law to report to potential borrowers? why might this rate be misleading to an uninformed borrower?

-calculate APR -required to report APR= 13.28% -this is deceptive because the borrower is actually paying annualized interest of 14.2%/year not the 13.8% reported in the loan contract

a bank charges 10.1% compounded monthly on its loans; another bank charges 10.3% compounded semiannually. as a borrower, which one would you go to for a loan?

-calculate EAR -first bank: 10.58% -second bank: 10.57% -for a borrower, the one with the higher EAR would be preferred -so first bank preferred -the higher APR doesn't always mean the higher EAR! -the number of compounding periods within a year will also affect the EAR

investors POV: would you be willing to pay $24,099 today in exchange for $100,000 in 30 years? what would you consider in answering yes or no? would you answer depend on who's making the promise to repay

-consideration: based on opportunity cost; is the rate of return implicit in the offer attractive relative to other, simple risk investments? -the rates offered on investments reflect the perceived risk of the investment -decision: calculate what you'd earn --> the IRR! -if other altneratives offer les than 4.86% then take this investment -if they offer you more than 4.86%, take that other alternative

A life insurance co. is trying to sell you an investment policy that will pay you and your heirs $30k per year forever. if the required return on this investment is 5%, how much will you pay for the policy?

-do PV=C/r -solve for PV

stated annual interest rate

-interest rate stated on an annual basis

discounting

-inverse of compounding -to determine the present value of a future amount received several periods in the future

what happens to the future value of an annuity if you increase the rate, r? what happens to the PV?

-just as increasing the interest rate increases the FV of a single cash flow and reduced the PV of an individual cash flow, assuming positive cash flows and a positive interest rate, the FV of the annuity will risk and the PV of an annuity will fall

if prices rise...? if price drops...?

-rate of return drops -rate of return rises

annuity

-series of regular intervals for a defined period of time -annuities are a steam of regular payments at regular intervals -rent, salary, pensions, car payments -each of the cash flows in the annuity acts in the same way as individual cash flows -take different forms based on whether the cash flows appear at the beginning or end of each period and whether each cash flow is the same of the cash flows grow at a given rate

EAR

-the annual interest rate that reflects the impact of intra-year compounding

let's say you deposit a large sum of money in an account that earns a low interest rate and simultaneously deposit a small sum in an account with a high interest rate. what account will have the larger future value?

-the large deposit will have a larger FV for some period -but after time, the smaller deposit with the larger interest rate will eventually become larger due to the effect of compound interest -the length of time for the smaller deposit to overtake the larger deposit depends on the amount deposited in each account and the interest rate

if you were an athlete negotiating a conctract with a signing bonus of $1 million, would you want the bonus payed immediately? or divided into smaller payments over the duration of your contract? how about looking at it from the team's perspective?

-the nominal value= $1 million; the economic value of the contract depends on how the cash is actually paid -spreading out the payments would make the economic value of the bonus smaller; they want it today -for the owner of the team, this would be great; given a fixed amount, splitting it up into future payments means that the economic value of the payments to the athlete are smaller

the TMCC security is traded on an exchange. if you looked at the price today, doo you think the price would exceed the $24,099 original price? why? holding all economic risk factors constant, if you looked in 2028, do you think the price would be higher or lower than today's price? why?

-today: we would say that the price in the market would be the same as the economic value calculated; $24,099, because the US capital markets are reasonably efficient -in 10 years: given the assumptions that nothing changes, the price would be higher because as time passes the price of the security will tend to rise toward $100k

compounding

-when the interest earned each year is applied to the principal -the exponential increase in the value of an investment because interest earned is added to the principal, which produces an increased payment in the subsequent period -process of determining the FV of an investment

should lending laws be changed to require lenders to report EARs instead of APRs? why or why not?

-with annual compounding these rates are the same; however, for compounding more frequently than annually, they are different -answer: YES -APRs don't generally provide the relevant rate; the only advantage is that they're easier to compute (but technology) -APRs on debt generally look more attractive than the true rate charged

FV factor

= (1+r)^T

PV factor

= 1/(1+r)^T

EAR equation

EAR=[ 1+ r/m]^m - 1

FV equation

FV=PV(1+r)^n

FV of annuity equation

FVA= C{[(1+r)^t - 1] / r}

PV of a perpetuity

PV= C/r

PV equation

PV= FV/(1+r)^n

PV of annuity equation

PVA= C({1-[1/(1+r)^t]} / r)

multiple cash flows at multiple times...

are composed of individual cash flows that follow the same time value logic as the individual amounts that we examined in the lesson

period interest rate

interest per period

APR equation

m [(1 + EAR)^1/m - 1]

interest rate equation

r= (FV/PV^1/t -- 1

opportunity cost equation

risk free rate + risk premium

calculating number of periods

t= ln (FV/PV)/ ln (1+r)

as the length of the annuity payments increases...

the PV of the annuity approaches the PV of the perpetuity

the higher the risk premium...

the larger the interest rate and the lower the PV

as time passes...

the time until receipt of the $100k grows shorter, and the PV rises

a treasury security should offer a lower rate of return since...

there is no risk premium