week 8 (module 7) - liability analysis Flashcards
what is the concept of timevalue of money?
a dollar today is worth more than a dollar tomorrow (somewhere in the future)
if we invest the dollar now, we would have the dollar and interest on the dollar
what generalizations do risk and interest factors yield?
- the right to receive an amnt now (pv) is worth more than the right to receive the same amnt later (fv)
- the longer we wait to receive an amnt, the less attractive it is
- the greater the interest rate, the greater the amnt we will receive in the future
- the more risk associated with a cash flow, the higher the interest rate.
if you have 90.91 today, adn can invest it at 10% for one year, our investment will grow to be:
100 dollars
90.91 is the pv of 100 dollars in a year
how to calculate the pv of a single payment
pv of a single payment = future amnt * 1/(1+i)^n
how do you use the pv tables?
- determine # of interest compounding periods (3 years comp. semiann = 6 periods)
- extreme left hand column indicates # of periods
- important to distinguish between years and comp. periods
- table is for comp. periods (years * # of comp. periods per year) - determine interest rate per comp. period
- int rates are usually quoted on per year basis
- rate per compounding period is annual rate / # of comp. periods per year (ex. 10% ann rate would be 10% per period is comp. annually and 5% per period is semiann) - locate pv factor, which is at the intersection of row of appropriate number of compounding periods and the column of the appropriate int rate per compounding period
- multiply factor by $ that will be paid/received in future
compute the pv of 100 to be received 1 year from today discounted at 10% sem ann
of periods (one y, semi ann) = 2
rate per period (10%/2) = 5%
multiplier = 0.90703
pv = 100 * 0.90703 = 90.70
compute the pv of 100 to be received 2 years from today, discounted at 10% compounded semiannually
of periods (2 y, semi ann) = 4
rate per period (10%/2) = 5%
multiplier = 0.82270
pv = 100 * 0.82270 = 82.27
how many cash flows does a bond have?
interest payments + principal payment
what is an annuity
when future cash flows involve the same amnt being paid/received every period
ex. semi ann int payments on bonds, quarterly dividend receipts, monthly insurance premiums
if payment/receipt is equally spaced over time and each cash flow is the same $ amnt, we have an annuity
if 100 is to be received at the end of each of the next 3 years as an annuity, what is the pv of this annuity? (5% ann rate)
y1: 100 * 0.95238 = 95.24
y2: 100 * 0.90703 = 90.70
y3: 100 * 0.86384 = 86.38
total = 272.32
use pv of single amount table of the same percentage but for different years going down with accordance with the period
use pv of annuity table - easier
what is a bond certificate?
purchasers of bonds receive it
specifies:
- issuing comp name
- face value (maturity vlaue, par value, principal)
- maturity date (date when issuing comp is obligated to pay back debt)
- coupon rate (stated interest rate), rental fee on borrowed money
- interest payment dates (dates that interest payments are due, gen 2x a year)
- bond date
what does a bond agreement specify?
series of interest payments (cash outflow)
single payment of face vlaue at maturity
what rate do we use to determine a bond’s market vlaue (its price)?
market rate on the date of the sale
how is the selling price of a bond determined?
- use table of pv of single payments to compute pv of future principal payment at prevailing market rate
- use pv of annuity table to compute pv of future series of interest payments (annuity) at prevailing market rate
- add pv from steps 1 and 2
at what price are bonds sold at?
market price, the amount invetsors are willing to pay -> market price is bond’s pv
what interest rates set bond price?
- stated interest rate (coupon rate)
- printed on bond certificate
- determines interest payment amnt to bondholders - market interest rate (effective interest rate)
- demanded by investors for loaning money
- varies minute to minute
in most cases, when a comp issues a bond, interest rates differ because of time that passes between when a bond issue is established and when it’s actually sold
example: par bond
determine the price of a 100k, 8%, 4 year bond paying interest semi annually
bond sold when the prevailing market rate as 8% (4% semi annually)
use 4% interest rate
- single payment price - 100k (table 1)
100k * 0.73069 = 73,069 - interest payments - 4k/period (table 2)
4k * 6.73274 = 26,931
pv = 73069 + 26391 = 100k
example: discount bond
determine price of 100k, 8%, 4 year bond paying interest semiann
bond sold when prevailing market rate was 10% (5% semiann)
use 5% interest rate
- 100k * 0.67684 = 67684
- 4k * 6.46321 = 25853
pv = 67684 + 25853 = 93537
ex. premium bond
determine price of 100k, 8%, 4 year bond paying interest semiann
bond sold when prevailing market rate was 6% (3% semiann)
use 3% discount rate for tables
use 4% rate to determine amount for interest payments
- 100k * 0.78941 = 78941
- 4k * 7.01969 = 28079
pv = 78941 + 28079 = 107020
*** in gen, bonds sell at premium whenever coupon rate is greater than market rate
what is the effective rate of a bond?
always equals yield (market rate) demanded by investors, regardless of bond’s coupon rate
companies cannot influence effective cost of debt by raising/lowering coupon rate
coupon rate > market rate -> bond sells at premium
coupon rate = market rate -> bond sells at par
coupon rate < market rate -> bond sells at discount
what is the difference between interest expense and interest payments
effective cost of debt is used to determine interest expense reported in income statement
due to premiums and discounts, interest expense is usually diff from cash interest paid
how to account for issuing bonds at par
if a comp issues 50k, 6%, 5 year bonds at par on Jan 1, 2023 that pay semi annually at Jan 1 and July 1
issuance:
Jan 1, 2023
DR cash (50k)
CR bonds payable (50k)
- to determine cash interest payment, multiply face value of bond by coupon rate then half it
(50k * 0.06)/2 = 1500
semi-ann payments
July 1, 2023
DR interest expense (1500)
CR cash (1500)
AJE at year end to accrue interest expense:
Dec 31, 2023
DR interest expense (1500)
CR interest payable (1500)
At maturity:
Jan 1, 2028
DR bond payable (50000)
CR cash (50000)
A company issued a 5-year bond at par for $960 million, with no principal payments required until maturity. One year later, the bond is quoted at 82. What is the current market value of the bond?
quoted at 82 means it is valued at 82% of face value
face value is issued amnt (960 mill)
market value = face value * (quoted price/100)
= 960 * 82/100 = 960 * 0.82 = 787.2 mill
how to account for issuing bonds at a discount
if a corp issued 100k of 9%, 5 year semiann payment bonds when the market interest rate is 10%
- market price of bond drops and corp receives 96149 at issuance
Jan 1, 2023
DR cash (96149)
DR discount on bonds payable (3851)
CR bonds payable (100k)
how to account for issuing bonds at a premium
if a corp issues 100k of 9%, 5 year semi ann payment bonds when the market interest is 8%
- market price of bonds increases and corp receives 104100 at issuance
Jan 1, 2023
DR Cash (104100)
CR premium on bonds payable (4100)
CR Bonds payable (100k)
what happens to the balance of the discount account and premium account over the life of the bond issue (issuance date until maturity)?
amortized!
discounts:
- discount is allocated to interest expense thru amort each period over term of bond
- discount on bonds INCREASES bonds interest expense each period over term of bonds
premiums:
- premium is allocated to interest exp thru amort each period over term of the bond
- premium on bonds DECREASES bonds interest expense each period over term of bonds
if on jan 1, 2023, a corp issued 100k of 9%, 5 year bonds when the market interest rate is 10%
calculate interest expense based on effective interest rate method (discount)
issue date: jan 1, 2023
face value: 100k
stated interest rate: 9%
interest payments: semi ann
maturity date: jan 1, 2028
market interest rate: 10%
issue price: 96149
set up an amortization table for bonds showing interest payments, interest expense, discount amortization, discount balance, bond carrying amnt for each interest payment date
** memorize table
Jul 1, 2023
DR Interest expense (4807)
CR Discount on bonds payable (-XL) (307)
* discount ammortization
CR Cash (4500)
Dec 31, 2023
DR Interest expense (4823)
CR Discount on bonds payable (323)
CR Interest payable (4500)
B/S
LT liabilities:
Bonds payable 100k
Less: Discount on bonds payable
how would discount bond amort. be represented on a graph?
interest payment remains constant, interest expense increases over bond terms
space between lines represent discount ammort
bond carrying amount begins at bond price and gradually increase each period until it equals face value
if on jan 1, 2023, a corp issued 100k of 9%, 5 year bonds when the market interest rate is 9%
calculate interest expense based on effective interest rate method (premium)
issue date: jan 1, 2023
face value: 100k
stated interest rate: 9%
interest payments: semi ann
maturity date: jan 1, 2028
market interest rate: 8%
issue price: 104100
** memorize table
differences:
- premium amort = a-b, not b-a
- bond carrying amnt = bv - c not bv + c
Jul 1, 2023
DR Interest Expense (4164)
DR Premium on bonds payable
(premium amort)
CR cash (4500)
Dec 31, 2023
DR Interest expense (4151)
DR Premium on Bonds Payable
CR Interest payable (4500
B/S
LT Liabilities:
Bonds Payable (100k)
Add: Premium on bonds payable (3415)
how would premium bond amort. be represented on a graph?
interest payment remains constant while interest expense decreases over bond terms
space between two lines reps prem amort
bond carrying amount begins at bonds price and decreases each period until it equals face value
how to calculate gain or loss on bond repurchase?
gain or loss on bond repurchase = net bonds payable - repurchase payment
net bonds payable = book value/carrying value, amnt reported on b/s
report LOSS on i/s if:
issuer pays more to retire bonds than amnt carried on b/s
report GAIN on i/s if:
the repurchase price is LESS than net bonds payable
what are the f/s effects of bond repurchase (bond redemption/extinguishment)
gain or loss usually results
