Question

1. Derek borrows $324,738.00 to buy a house. He has a 30-year mortgage with a rate of 4.73%. After making 132.00 payments, how much does he owe on the mortgage?

2.Caspian Sea Drinks needs to raise $34.00 million by issuing bonds. It plans to issue a 16.00 year semi-annual pay bond that has a coupon rate of 5.00%. The yield to maturity on the bond is expected to be 4.78%. How many bonds must Caspian Sea issue? (Note: Your answer may not be a whole number. In reality, a company would not issue part of a bond.)

Answer 1

Part 1:

EMI :
EMI or Instalment is sum of money due as one of several equal payments for loan/ Mortgage taken today, spread over an agreed period of time.

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Particulars	Amount
Loan Amount	$          324,738.00
Int rate per Month	0.3942%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 324738 / PVAF (0.0039 , 360)
= $ 324738 / 192.1442
= $ 1690.07
Outstanding balance after 132 payments:

Particulars	Amount
Loan Amount	$ 324,738.00
Int rate per Month	0.3942%
No. of Months	360
Outstanding Bal after	132
EMI	$      1,690.07
Payments Left	228

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1690.07 * [ 1 - ( 1 + 0.003942 ) ^ - 228 ] / 0.003942
= $ 1690.07 * [ 1 - ( 1.003942 ) ^ - 228 ] / 0.003942
= $ 1690.07 * [ 1 - 0.407818 ] / 0.003942
= $ 1690.07 * [ 0.592182 ] / 0.003942
= $ 253888.64

r = Int Rate per period
n = Balance No. of periods

Part 2:

Bond Price:
It refers to the sum of the present values of all likely coupon payments plus the present value of the par value at maturity. There is inverse relation between Bond price and YTM ( Discount rate ) and Direct relation between Cash flow ( Coupon/ maturity Value ) and bond Price.

Price of Bond = PV of CFs from it.

Period	Cash Flow	PVF/ PVAF @2.39 %	Disc CF
1 - 32	$      25.00	22.1911	$    554.78
32	$ 1,000.00	0.4696	$    469.63
Bond Price			$ 1,024.41

As Coupon Payments are paid periodically with regular intervals, PVAF is used.
Maturity Value is single payment. Hence PVF is used.

Periodic Cash Flow = Annual Coupon Amount / No. times coupon paid in a year
Disc Rate Used = Disc rate per anum / No. of times coupon paid in a Year

What is PVAF & PVF ???
PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Anum
Where n is No. of Years

How to Calculate PVAF using Excel ???
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

No. of bonds to be issued = Amount Required / Bond Price

= $ 34000000 / $ 1024.41

= 33190

33190 binds to be issued to procure the required amount.