ProTeck Ltd$.$ operates under ideal conditions of uncertainty. The company began operations by buying a machine to produce its specialized product. The machine is expected to last for $3$ years, with no salvage value. Purchase of the machine was partly financed by a bank loan of $$50,000$ and the balance from the proceeds of a capital stock issue. The bank loan must be repaid in three equal instalments including interest $($Hint: you may wish to prepare a blended payment schedule$).$

Cash flows from the product depend on the state of the economy, and are received at year end. The details about the cash flows, the states of nature and the associated objective state probabilities are as follows:

Cashflow

State

Probability

Year $1$

Year $2$

Year $3$

High

$0\mathrm{.}30$

$$120,000$

$$150,000$

$$100,000$

Medium

$0\mathrm{.}45$

$90,000$

$100,000$

$80,000$

Low

$0\mathrm{.}25$

$60,000$

$80,000$

$60,000$

ProTeck$$s cost of capital is $7\%$ per annum. The company plans to pay a dividend of $$10,000$ at the end of years $1$ and $2,$ with the remaining cash distributed at the end of year $3.$ During year $1,$ the high state is achieved. The state realization in year $2$ is low.

Required:

a$)$ Describe briefly what is meant by ideal conditions of uncertainty. Also explain why ideal conditions do not exist in real life. $[3$ marks$]$

b$)$ Calculate the value of initial investment required by PQR Ltd $[4$ marks$]$ c$)$ Prepare a blended loan repayment schedule $[3$ marks$]$

d$)$ Prepare a comparative income statement using the accretion of discount format for PQR for the years ended December $31,20$x$1$ and $20$x$2[6$ marks$]$

e$)$ Prepare, in good form, a balance sheet for PQR as at December $31,20$x$2.[7$ marks$]$