Question

A bank offers you a $1M loan with an IRR of 3%. (Recall from class that in this case you can interpret the IRR as a “borrowing rate”.) The bank asks you to repay the loan in 8 equal annual installments. (a) What is the annual repayment on the loan? (b) What is the NPV of the loan if your opportunity cost of capital is 10%?

Answer 1

Part A:

Particulars	Amount
Loan Amount	$       1,000,000.00
Int rate per Anum	3.0000%
No. of Years	8

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 1000000 / PVAF (0.03 , 8)
= $ 1000000 / 7.0197
= $ 142456.39

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

Part B:

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Particulars	Values
Initial Outflow	$      -1,000,000.00
Start Year	1
End Year	8
Disc Rate	10.00%
Cash Flow per anum	$           142,456.39

NPV:

Year	Cash Flow	PVF @10 %	Disc CF
0	$         -1,000,000.00	1.0000	$        -1,000,000.00
1 - 8	$              142,456.39	5.3349	$            759,994.33
NPV			$           -240,005.67

PVAF calculation in Excel:
=PV(Rate,NPER,-1)
Rate - Disc rate
NPER - No. of years