rennin dairy corporation is considering a plant expansion decision that has an estimated useful life of 20…

Brief Explanations:

1. Internal Rate of Return (IRR): IRR is the discount rate that makes the net present value (NPV) of a project zero. Salvage value is a cash inflow at the end of the project (year 20 here). A decrease in salvage value reduces the total cash inflows. To make NPV = 0, the IRR (which discounts cash flows) would be affected? Wait, no—wait, the payback period and IRR logic:

   • Payback Period: Payback period is the time to recover initial investment, based on annual cash inflows (not salvage value, which is at year 20). Since payback focuses on recouping initial outlay from annual operating cash flows (before year 20), a change in salvage value (year 20) does not affect the payback period (which is 9.6 years, <20 years). So payback period has no effect.
   • IRR: Wait, no—salvage value is a terminal cash flow. If salvage value decreases, the total cash inflows (sum of annual cash flows + salvage) decrease. The IRR is the rate where NPV = 0. If cash inflows (including salvage) decrease, the IRR would... Wait, no, wait: Let’s re-express. The IRR is calculated by solving for ( r ) in:
     ( \text{Initial Investment} = \sum_{t=1}^{19} \frac{\text{Annual Cash Flow}}{(1 + r)^t} + \frac{\text{Annual Cash Flow} + \text{Salvage Value}}{(1 + r)^{20}} )
     If salvage value decreases, the right-hand side (RHS) of the equation decreases (since the last term is smaller). To make RHS = Initial Investment (left-hand side, LHS), we need a lower ( r )? Wait, no—wait, if cash inflows (including salvage) are lower, the IRR (the rate that equates PV of inflows to outflows) would actually... Wait, no, maybe I got it wrong. Wait, no—payback period: payback is about recouping initial investment from annual operating cash flows (before the final year’s salvage). Since the payback period is 9.6 years (less than 20), the salvage value (at year 20) is not part of the payback calculation (payback is done by year 9.6). So payback period is unaffected.

   For IRR: Wait, no—if salvage value decreases, the total cash inflows (over 20 years) decrease. The IRR is the rate where NPV = 0. If cash inflows are lower, the IRR (the discount rate that makes NPV zero) would... Wait, no—let’s think of NPV formula:
   ( \text{NPV} = -\text{Initial Investment} + \sum_{t=1}^{19} \frac{CF_t}{(1 + r)^t} + \frac{CF_{20} + \text{Salvage}}{(1 + r)^{20}} )
   If salvage decreases, the last term decreases. So to have NPV = 0 (IRR), we need a lower ( r )? Wait, no—if the cash inflows (including salvage) are lower, the IRR (the rate that makes PV of inflows = outflows) would actually decrease? Wait, no, maybe I confused. Wait, no—let’s take a simple example: Suppose initial investment is $100, annual cash flow is $10 for 19 years, and salvage is $20 at year 20. IRR is the rate where $100 = 10*(P/A, r, 19) + 20*(P/F, r, 20). If salvage becomes $10, then the equation is $100 = 10*(P/A, r, 19) + 10*(P/F, r, 20). The RHS is now smaller for the same ( r ), so we need a lower ( r ) to make RHS = 100? Wait, no—if RHS is smaller, we need a lower discount rate (r) to increase the present value of the cash flows (since lower r means higher PV of future cash flows). Wait, no—discount rate and PV are inversely related. So if cash inflows (including salvage) decrease, the IRR (the rate that makes PV of inflows = outflows) would actually decrease? Wait, no, maybe I have it backwards. Let’s take a concrete number. Suppose initial investment is $100, annual cash flow is $10 for 20 years (no salvage), IRR is the rate where 100 = 10*(P/A, r, 20). (P/A, r, 20) = 10, so r ≈ 7.75%. If we add salvage of $100 at year 20, then 100 = 10*(P/A, r, 19) + 110*(P/F, r, 20). The IRR here would be higher, because we have an extra $100 at year 20. So if we decrease salvage, the IRR would decrease? Wait, no—if salvage increases, IRR increases; if salvage decreases, IRR decreases. But wait, in the problem, the payback period is 9.6 years, which is less than 20, so the payback is achieved by year 9.6, meaning the salvage value (at year 20) is not part of the payback calculation (payback is about recouping initial investment from annual cash flows before year 20). So payback period is unaffected.

   So:

   • Payback Period: No effect (because payback is based on annual cash flows before the final year’s salvage; since payback is 9.6 years <20, salvage doesn’t impact payback).
   • IRR: Decreases (because salvage value is a cash inflow; decreasing it reduces total cash inflows, so the IRR (the rate that equates PV of inflows to outflows) decreases).

   Wait, but the options: Let’s check the options. Option C: IRR Decrease, Payback No Effect. Wait, but earlier I thought IRR decreases, payback no effect. Wait, let’s re-express:

   • Payback Period: Payback is the time to recover initial investment from annual operating cash flows (not including salvage, because salvage is at year 20, and payback is 9.6 years, so by year 9.6, the initial investment is already recovered. So salvage value (at year 20) does not affect the payback period. So payback period: No Effect.

   • IRR: Salvage value is a cash inflow at year 20. If salvage value decreases, the total cash inflows (sum of annual cash flows + salvage) decrease. The IRR is the rate where NPV = 0. If cash inflows are lower, the IRR (the discount rate that makes PV of inflows = outflows) will decrease (because lower cash inflows mean the required discount rate to make NPV zero is lower? Wait, no—wait, NPV = PV(inflows) - PV(outflows). If inflows (including salvage) decrease, PV(inflows) decreases. So to have NPV = 0, we need a lower discount rate (IRR) to increase PV(inflows) (since lower discount rate increases PV of future cash flows). Wait, no—discount rate and PV are inversely related. So if PV(inflows) is too low (because salvage is lower), we need a lower discount rate to make PV(inflows) higher (so that PV(inflows) = PV(outflows)). Therefore, IRR decreases.

   So IRR: Decrease; Payback Period: No Effect. Which matches Option C. Wait, but the original selected option was B, which is wrong. Wait, maybe I made a mistake. Let’s re-express:

   Payback period: The payback period is calculated as the time it takes for the cumulative annual cash flows (excluding salvage, because salvage is at the end) to equal the initial investment. Since the payback period is 9.6 years (less than 20), the salvage value (at year 20) is not part of the payback calculation (because by year 9.6, the initial investment is already recovered). So a change in salvage value (at year 20) does not affect the payback period. So payback period: No Effect.

   IRR: The IRR is the rate that makes the NPV of all cash flows (initial investment, annual cash flows, and salvage value) equal to zero. If salvage value decreases, the total cash inflows (over the project’s life) decrease. Therefore, the IRR (the rate that equates the present value of inflows to the present value of outflows) will decrease (because lower cash inflows mean the required discount rate to make NPV zero is lower). Wait, no—wait, if cash inflows are lower, the IRR (the discount rate that makes NPV = 0) will actually decrease? Let’s take a simple example:

   Example 1: Initial investment = $100, annual cash flow = $10 for 20 years, salvage = $0.
   NPV formula: ( -100 + \sum_{t=1}^{20} \frac{10}{(1 + r)^t} = 0 )
   The IRR here is the rate where the present value of 20 annual $10 cash flows equals $100. Using the annuity formula, ( 100 = 10 \times \frac{1 - (1 + r)^{-20}}{r} ). Solving for ( r ), we get ( r \approx 7.75% ).

   Example 2: Same as Example 1, but salvage = $50 (at year 20).
   NPV formula: ( -100 + \sum_{t=1}^{19} \frac{10}{(1 + r)^t} + \frac{10 + 50}{(1 + r)^{20}} = 0 )
   The IRR here will be higher than 7.75% because we have an extra $50 at year 20.

   Example 3: Same as Example 2, but salvage = $25 (decrease from $50).
   The IRR here will be lower than the IRR in Example 2 (because we have less cash inflow at year 20).

   So decreasing salvage value decreases the IRR. And payback period is unaffected (since payback is based on annual cash flows before year 20). Therefore, the correct option is Choice C (Decrease in IRR, No Effect on Payback Period).

Answer:

Choice C