Question

Consider the following:

–       You need a $300,000 financing package.

–       $150,000 at 9%, 30 Years

–       $100,000 at 8%, 20 Years

–       $50,000 at 7% 10 Years

1. What is the monthly payment for each part of the financing package?
2. What is the IRR on the $300,000 borrowed?

Does anybody know how to solve these two questions with details?

Answer 1

Principal(P)	n	i	r = i/m	1+r	(1+r)^-mn	1- [(1+r)^-n]	PVAF = [1- [(1+r)^-n]] /r	Monthly Installment
$ 150,000	30	9%	0.75%	1.0075	0.0679	0.9321	10.3567	$              14,483.42
$ 100,000	20	8%	0.67%	1.0067	0.2030	0.7970	9.9625	$              10,037.64
$    50,000	10	7%	0.58%	1.0058	0.4976	0.5024	7.1771	$                 6,966.56

where, m = Frequency of Compounding = Monthly = 12

Computation of IRR:

Let us discount at 8.5%

Years	Monthly Installment	PVAF	PV of Installment
1 - 10 Years	$   31,487.63	6.7212	$ 211,633.89
11 - 20 Years	$   24,521.07	2.8812	$    70,649.52
21 - 30 Years	$   14,483.42	1.2353	$    17,891.29
-	PV of Installment	-	$ 300,174.70

As the PV of Installments at 8.5% is pproximately equal to Loan Amount($300,000), IRR = 8.5%

Computation of PVAF

n	i	r = i/m	1+r	(1+r)^-mn	1- [(1+r)^-n]	PVAF = [1- [(1+r)^-n]] /r
10	8.50%	0.71%	1.0071	0.4287	0.5713	6.7212
20	8.50%	0.71%	1.0071	0.1838	0.8162	9.6024
30	8.50%	0.71%	1.0071	0.0788	0.9212	10.8376

PVAF(11-20 Years) = PVAF(20 Years) - PVAF(10 Years) = 2.8812

PVAF(21-30 Years) = PVAF(30 Years) - PVAF(20 Years) = 1.2353